maths rounding problem solving

Rounding Numbers

What is "rounding" .

Rounding means making a number simpler but keeping its value close to what it was.

The result is less accurate, but easier to use.

Example: 73 rounded to the nearest ten is 70 , because 73 is closer to 70 than to 80. But 76 goes up to 80.

Common Method

There are several different methods for rounding . Here we look at the common method , the one used by most people:

"5 or more rounds up"

First some examples (explanations follow):

How to Round Numbers

• Decide which is the last digit to keep
• Leave it the same if the next digit is less than 5 (this is called rounding down )
• But increase it by 1 if the next digit is 5 or more (this is called rounding up )

Example: Round 74 to the nearest 10

• We want to keep the "7" (it is in the 10s position)
• The next digit is "4" which is less than 5, so no change is needed to "7"

(74 gets "rounded down")

Example: Round 86 to the nearest 10

• We want to keep the "8"
• The next digit is "6" which is 5 or more, so increase the "8" by 1 to "9"

(86 gets "rounded up")

When the first digit removed is 5 or more, increase the last digit remaining by 1.

Why does 5 go up ?

5 is in the middle ... so we could go up or down. But we need a method that everyone agrees to.

Think about sport: we should have the same number of players on each team, right?

And that is the "common" method of rounding. Read about other methods of rounding .

A farmer counted 87 cows in the field, but when he rounded them up he had 90.

Rounding Decimals

First work out which number will be left when we finish.

• Rounding to tenths means to leave one number after the decimal point.
• Rounding to hundredths means to leave two numbers after the decimal point.

3.1416 rounded to hundredths is 3.14

as the next digit (1) is less than 5

3.1416 rounded to thousandths is 3.142

as the next digit (6) is more than 5

1.2735 rounded to tenths is 1.3

as the next digit (7) is 5 or more

To round to "so many decimal places" count that many digits from the decimal point:

1.2735 rounded to 3 decimal places is 1.274

as the next digit (5) is 5 or more

Rounding Whole Numbers

We may want to round to tens, hundreds, etc, In this case we replace the removed digits with zero.

134.9 rounded to tens is 130

as the next digit (4) is less than 5

12,690 rounded to thousands is 13,000

as the next digit (6) is 5 or more

15.239 rounded to ones is 15

as the next digit (2) is less than 5

Rounding to Significant Digits

To round to "so many" significant digits, count digits from left to right , and then round off from there.

1.239 rounded to 3 significant digits is 1.24

as the next digit (9) is 5 or more

134.9 rounded to 1 significant digit is 100

as the next digit (3) is less than 5

When there are leading zeros (such as 0.006), don't count them because they are only there to show how small the number is:

0.0165 rounded to 2 significant digits is 0.017

Significant digit calculator.

(Try increasing or decreasing the number of significant digits. Also try numbers with lots of zeros in front of them like 0.00314, 0.0000314 etc)

We're sorry, but we don't support Internet Explorer anymore. Please use a different browser .

Rounding Whole Numbers & Decimals Online practice for grades 1-6

On this page, you can practice rounding whole numbers to the nearest ten, nearest hundred, nearest thousand, and so on. You can use this online practice for all elementary grades (grades 1-6).

This free, online practice program can also be installed offline as an app in your phone or tablet, depending on your browser and operating system. To install it, click on the "Add to home screen" button at the bottom of the page. On Android Chrome, click on the three dots, and then "Add to home screen". If you don't see the button or the "Add to home screen" option, then you probably cannot install this app in your browser.

Use these quick links for some common options for rounding practice for different grade levels.

1st and 2nd grades: round to the nearest ten, within 0-100

3rd grade: round to the nearest ten and nearest hundred, within 0-1,000

3rd grade: round to the nearest thousand, within 0-10,000

4th grade: round to any place, within 0-1,000,000

5th grade: round to any place, within 0-1,000,000,000

5th grade: round decimals (up to 3 decimal digits)

6th grade: round decimals (up to 6 decimal digits)

Generate Quick Link

• Parallelogram
• Quadrilateral
• Parallelepiped
• Tetrahedron
• Dodecahedron
• Fraction Calculator
• Mixed Fraction Calculator
• Greatest Common Factor Calulator
• Decimal to Fraction Calculator
• Whole Numbers
• Rational Numbers
• Place Value
• Irrational Numbers
• Natural Numbers
• Binary Operation
• Numerator and Denominator
• Order of Operations (PEMDAS)
• Scientific Notation

Table of Contents

Last modified on October 11th, 2023

#ezw_tco-2 .ez-toc-title{ font-size: 120%; ; ; } #ezw_tco-2 .ez-toc-widget-container ul.ez-toc-list li.active{ background-color: #ededed; } chapter outline

Rounding numbers.

Rounding number is the process of approximating the number to its closest value. It involves reducing the number of significant digits while retaining the general magnitude or size of the original number. The result of rounding is less accurate than the original number but simplifies calculations.

Suppose one of your friends covered 18 km while returning home from his office. But, when documenting the distance covered in paper, he estimated it as 20 km.

You may wonder where that extra 2 km comes from. We can explain it this way:

18 is closer to 20 than 10. So it is rounded off to 20. If the value would have been 14 km, the value would have approximated to 10 km.

But what if the value is 15 km? It would also go up and be approximated to 20 km. So, any value that equals or exceeds 15 will go up to 20, and values below 15 will round down to 10.

We follow the following three steps while rounding a number:

• Identifying the rounding digit
• When rounding down, we keep it the same if the next digit is less than 5
• When rounding up, we increase it by 1 if the next digit is 5 or more than 5

Rounding to the Nearest Ten

Here, we need to check the digit to the right of the tens place, the ones place.

For example, rounding the number 147, the one’s digit 7 is ˃5, so we add 1 to the tens digit (4 + 1 = 5), and the digit becomes 150.

Rounding to the Nearest Hundred

Here, we check the digit to the right of the hundreds place, the tens place.

For example, when rounding the number 568 to its nearest hundred, the tens digit is 6, which is ˃5, so we add 1 to the hundred digits (5 + 1 = 6). The remaining two digits at the ones and the tens placed will be 0. So, 568 becomes 600 after rounding.

Rounding to the Nearest Thousands

Here, we check the digit to the right of the thousands place, that is, the hundreds place.

For example, when rounding the number 7892 to its nearest thousands, the tens hundreds is 8, which is ˃5, so we add 1 to the thousands digit (7 + 1 = 8), and the rest three digits at the ones, tens, and hundreds place will both be 0. So, 7892 becomes 8000 after rounding.

Rounding Negative Numbers

But how can we round a negative number? The number -8.5 can be rounded to -9 or -8, but which one to follow?

It is again up to us which process we want to follow: rounding up or rounding down.

Rounding Decimals

Like rounding whole numbers, we follow the same steps here.

Rounding to the Nearest Tenths

Here, we need to check the digit to the left of the tens place, the Hundredth place. Thus, rounding to tenths leaves one number after the decimal point.

For example, when 4.57 is rounded to the nearest ten, it becomes 4.6, and 14.87 is rounded to 14.9

Rounding to the Nearest Hundredths

Here, we need to check the digit to the left of the hundredth place, the thousandth place. Thus, rounding to hundredths leaves two numbers after the decimal point.

For example, 0.6278 is rounded to 0.63, and 1.8743 is rounded to 1.87

Rounding to the Nearest Thousandths

Here, we need to check the digit to the left of the thousandth place. Thus, rounding to hundredths leaves three numbers after the decimal point.

For example, 0.5679 is rounded to 0.568and 6.3859is rounded to 6.386

There are several methods of rounding numbers. While rounding, we either round up or round down to indicate whether the number has increased or decreased after rounding.

Half Round Up

In this method of rounding, 0.5 goes up. Thus, 9.5 rounds up to 10.

• 4.5 rounds up to 5
• 9.9 rounds up to 10
• 5.3 rounds down to 5

Half Round Up with Negative Numbers

• -4.5 rounds up to -4
• -9.9 rounds down to -10
• -5.3 rounds up to -4

Half Round Down

But we can round 0.5 down as well. In such a case, 9.5 will round down to 9.

• 2.5 rounds down to 2
• 4.4 rounds down to 4
• 9.6 rounds up to 10

Half Round Down with Negative Numbers

• -2.5 rounds down to -3
• -4.4 rounds up to -4
• -9.6 rounds down to -10

All the above rounding methods are symmetric. As we can see, 4.5 rounds up to 5, so -4.5 should be rounded to -5.

However, some methods may need to be more symmetrical.

Round Half Away from Zero

It means rounding half the values away from zero. Here, the method has no biases towards positive or negative numbers but is biased away from zero. It involves rounding a half value towards the next integer, which is closer to positive or negative infinity on the basis of its value.

For example,

• 7.5 rounds to 8
• -7.5 rounds to -8

Round Half towards Zero

It is similar to rounding half away from zero but in the opposite direction. It has no bias towards a positive or a negative number. Still, it has a tendency towards 0, which means half the values will be rounded to the next integer closer to zero.

• 7.5 rounds to 7
• -7.5 rounds to -7

Round Half to Even

Rounding half to even is used as a tie-breaking rule as it has no biases towards a positive or a negative number or even towards or away from zero. Here, the half values are rounded to the nearest even integer.

• 5.5 rounds up to 6 (since 6 is an even number)
• 6.5 rounds down to 6 (since 6 is an even number)
• -6.5 rounds up to 7
• -8.5 rounds up to 8 (since 8 is an even number)

Round Half to Odd

It is also a tie-breaking rule, like rounding half to even. However, the number is rounded to the nearest odd integer for rounding half to odd.

• 5.5 rounds down to 5 (since 5 is an odd number)
• 7.5 rounds down to 7 (since 7 is an odd number)
• -8.5 rounds down to -9 (since 9 is an odd number)

Floor and Ceiling Method

These methods give the nearest integer down or up for floor and ceiling.

The number remains the same after rounding an integer.

So the floor of 6 is 6, and the ceiling of 6 is also 6.

However, depending on the method, the digit attains the nearest integer up or down for a decimal number.

For example, 2.7 is rounded down to 2 in the floor method, while it is rounded up to 3 in the ceiling method.   

Rounding Fractions

Rounding to fractions is the same as rounding decimals. We first convert the fraction into decimal and then round the number to tenths, hundredths, thousandths, and so on.

Rounding to Nearest Tenths

${\dfrac{14}{25}}$ is equal to 0.56, which, when rounded to the nearest tenths, gives 0.6

Rounding to Nearest Hundredths

${\dfrac{78}{48}}$ is equal to 1.625, which, when rounded to the nearest hundredths, gives 1.63

Rounding to Nearest Thousandths

${\dfrac{1823}{2000}}$ is equal to 0.9115, which, when rounded to the nearest thousandths, gives 0.912

Rounding to Significant Digits

A significant figure is each digit in a number that helps to express the number with the required degree of accuracy. For example, the number 15.6 has three significant figures.

There are specific rules for deciding the number of significant figures.

1) All nonzero digits are significant.

For example, 1.7 has 2 significant figures, and 2.678 has 4 significant figures.

2) Zeroes between nonzero digits are significant.

For example, 3006 has 4 significant figures, and 10.3 has 3 significant figures.

3) Zeroes to the left of the first nonzero digit are not significant.

For example, 0.002 has 1 significant figure, and 0.045 has 2 significant figures.

4) Zeroes to the right of a decimal point in a number are always significant.

For example, 0.045 has 2 significant figures, and 0.700 g has 3 significant figures.

5) For non-decimal numbers, the trailing zeros are not necessarily significant.

However, 280 can be written as 2 or 3 significant figures, and 60,700 may be 3, 4, or 5 significant figures. This ambiguity is removed by expressing the number in scientific notation. Depending on the number of significant figures, which is correct, 60,700 is written as:

• 6.07 × 104 calories (for 3 significant figures)
• 6.070 × 104 calories (for 4 significant figures)
• 6.0700 × 104 calories (for 5 significant figures)

Solved Examples

Round i) 767 ii) 34.68 to the nearest ten .

i) 767 on rounding to the nearest ten, give 770 ii) 34.68on rounding to the nearest ten, give 30

Round i) 8974 ii) 7646.89 to the nearest hundred .

i) 8974on rounding to the nearest hundred gives 9000 ii) 7646.89 on rounding to the nearest hundred gives 7,600

• Privacy Policy
• Trigonometry

Join Our Newsletter

© 2024 Mathmonks.com . All rights reserved. Reproduction in whole or in part without permission is prohibited.

Rounding & Estimation Word Problems

Related Pages Math Worksheets Lessons for Fourth Grade Free Printable Worksheets

Printable “Rounding Numbers” Worksheets: Round Numbers using the Number Line Round to nearest 10 Round to nearest 100 Round to nearest 1000, 10000, 100000 Rounding Word Problems

Rounding Word Problems Worksheets

In these free math worksheets, students practice how to use rounding to estimate and check the answers to word problems.

How to use estimation or rounding? Estimation or rounding is a useful tool for checking answers because it allows you to quickly determine if an answer is reasonable or not.

Here are some steps you can follow to use estimation to check an answer: Step 1: Make sure you understand what you are being asked to find and what information you have been given. Step 2: Round any numbers given in the problem to the nearest whole number, or to the nearest ten, hundred, or thousand, depending on the level of accuracy needed. Step 3: Use mental math to perform calculations quickly. For example, if you need to add 23 and 45, round them both to 20 and 50 and add those instead. This will give you an estimate that is close to the actual answer. Step 4: Once you have an estimate, compare it to the actual answer you calculated. If the estimate is close to the actual answer, you can be confident that your calculation is correct. If the estimate is significantly different from the actual answer, you may need to review your work and make corrections.

By using estimation to check your answers, you can catch errors early and avoid making mistakes that could lead to incorrect results.

Click on the following worksheet to get a printable pdf document. Scroll down the page for more Rounding Word Problems Worksheets .

More Rounding Word Problems Worksheets

Printable (Answers on the second page.) Rounding Worksheet #1 Rounding Worksheet #2 Rounding Worksheet #3 Rounding Worksheet #4 Rounding Worksheet #5

Online Round multi-digit number Worksheet #1

Rounding Multi-digit Numbers to any place value

Rounding Word Problems Use your estimated answer for part a) to check your answer for part b).

• For the bake sale, Connie baked 144 cookies. Esther baked 49 more cookies than Connie. a. About how many cookies did Connie and Esther bake? Estimate by rounding each number to the nearest ten before adding. b. Exactly how many cookies did Connie and Esther bake?
• Raffle tickets were sold for a school fundraiser to parents, teachers, and students. 563 tickets were sold to teachers. 888 more tickets were sold to students than to teachers. 904 tickets were sold to parents. How many tickets were sold to parents, teachers, and students? a. About how many tickets were sold to parents, teachers, and students? Round each number to the nearest hundred to find your estimate. b. Exactly how many tickets were sold to parents, teachers, and students?
• From 2010 to 2011, the population of Queens increased by 16,075. Brooklyn’s population increased by 11,870 more than the population increase of Queens. a. Estimate the total combined population increase of Queens and Brooklyn from 2010 to 2011. (Round the addends to the nearest thousand to estimate.) b. Find the actual total combined population increase of Queens and Brooklyn from 2010 to 2011.
• There were 3,905 more hits on the school’s website in January than February. February had 9,854 hits. How many hits did the school’s website have during both months? a. About how many hits (roud ro the nearest thousand) did the website have during January and February? b. Exactly how many hits did the website have during January and February?
• On Sunday, 77,098 fans attended a New York Jets football game. The same day 3,397 more fans attended a New York Giants game than the Jets game. How many football fans watched the Jets and Giants play on Sunday? a. Round each number to the nearest thousand to find an estimate of how many fans there are. b. What was the actual number of fans who watched the games?

Related Lessons & Worksheets

Round to nearest 10 (2-digit) (eg. 45 -> 50) Round to nearest 10 (3-digit) (eg. 725 -> 730) Round to nearest 100 (3-digit) (eg. 651 -> 700) Round to nearest 10 or 100 (3-digit)

Round to nearest 100 (4-digit) (eg. 2,754 -> 2,800) Round to nearest 1000 (eg. 3,542 -> 4,000) Round to nearest 10, 100, 1000

Round the nearest thousands

More Printable Worksheets

We welcome your feedback, comments and questions about this site or page. Please submit your feedback or enquiries via our Feedback page.

Rounding Numbers

Rounding numbers means adjusting the digits of a number in such a way that it gives an approximate value. This value is an easier representation of the given number. For example, the population of a town could be easily expressed as 700,000 rather than 698,869. Rounding numbers makes calculations simpler, resulting in a figure that is easy to remember. However, rounding of numbers is done only for those numbers where the exact value does not hold that much importance.

Let us learn more about rounding numbers, to get a better idea of how to round off a number to the nearest ten, hundred, thousand, and so on.

What is Rounding Numbers?

Rounding a number means the process of making a number simpler such that its value remains close to what it was. The result obtained after rounding off a number is less accurate, but easier to use. While rounding a number, we consider the place value of digits in a number.

Let us understand the concept of rounding through an example. Susan covered a distance of 2.05 miles, which she noted as approximately 2 miles. How did she estimate the approximate value of the distance she covered? Why didn't she record her distance as 3 miles? Noting an approximate and simpler value for a given number helps to make the analysis and calculations easier while using that number. Here, Susan noted an easier value to keep a record of the distance travelled by her.

Numbers can be rounded to different digits, like, they can be rounded to the nearest ten, hundred, thousand, and so on. For example, 541 rounded to the nearest hundred is 500 because 541 is much closer to 500 than 600. While rounding a number, we need to know the answer to the question,' What are we rounding the number to?' Suppose we need to round the number 7456. When 7456 is rounded to the nearest ten, it becomes 7460, but when 7456 is rounded to the nearest thousand, then it becomes 7000. A few examples like these are given below.

Rounding Numbers to the Nearest Ten

Rounding numbers to the nearest ten means we need to check the digit to the right of the tens place, that is the ones place. For example, when we round the number 7486 to the nearest ten, it becomes 7490.

Rounding Numbers to the Nearest Hundred

Rounding numbers to the nearest hundred means we need to check the digit to the right of the hundreds place, that is, the tens place. For example, when 7456 is rounded to the nearest hundred, it becomes 7500.

Round-Up and Round-Down

While rounding is a generic term, we usually use the terms, 'round up' or 'round down' to specify if the number has increased or decreased after rounding. When the rounded number is increased, then the given number is said to be rounded up, whereas, if the rounded number is decreased, then it is said to be rounded down.

Rules for Rounding Numbers

How do we decide which value is more appropriate between different approximated values of a number? Should we choose a number greater than the given number or go with the smaller one?

• We first need to know what our rounding digit is. This digit is the one that will ultimately be affected.
• After this, we need to check the digit to the right of this place which will decide the fate of the rounding digit.
• If the digit to the right is less than 5, we do not change the rounding digit. However, all the digits to the right of the rounding digit are changed to 0.
• If the digit to the right is 5 or more than 5, we increase the rounding digit by 1, and all the digits to the right of the rounding digit are changed to 0.

a.) If the bill at a furniture store comes to $3257, what is the rounded value of the amount to the nearest ten?

b.) If the bill comes to $3284, what would be the rounded value of this amount to the nearest ten?

a.) $3257 needs to be rounded to the nearest ten. So, let us mark the digit in the tens place, which is 5. Now, let us check the number to the right, which is 7 in this case. Since 7 is more than 5, we will replace 5 with 6, and all the digits to the right will become 0. So, $3257 is rounded to $3260.

b .) Here, $3284 needs to be rounded to the nearest ten. So, let us mark the digit in the tens place, which is 8. Now, let us check the number to the right, which is 4 in this case. Since 4 is less than 5, 8 will remain unchanged and the remaining digits to the right will change to 0. So, $3284 is rounded to $3280.

How to Round Off Whole Numbers?

Whole numbers are rounded off by following the same rules mentioned above. Let us apply the rules with the help of an example.

Example: Round 7234 to the nearest hundred.

• Step 1: Mark the place value up to which the number needs to be rounded. Here, 7234 needs to be rounded to the nearest hundred. So, we mark 2 which is in the hundreds place.
• Step 2: Observe and underline the digit to the right of 2, that is the tens place. Here, it is 3, so we will mark it as: 7 2 3 4
• Step 3: Compare the underlined digit with 5.
• Step 4: If it is less than 5, all the digits towards its right including it will be replaced by 0 while the digit in the hundreds place (2) will remain unchanged. Therefore, 7234 will be rounded to 7200.

Note: If the number to the right of 2 was 5 or greater than 5, then all the digits to the right of 2 would become 0, and 2 would be increased by 1 changing it to 3. For example, if the given number was 7268, then it would be rounded up to 7300 (to the nearest hundred).

How to Round Off Fractions?

Fractions are numerical values that represent a part of a whole. They are written in the form of (p/q), where q is not equal to zero. A simple rule to round fractions to the nearest whole number is to compare proper fractions to 1/2. In case if it is an improper fraction, we need to change it to a mixed fraction and then compare the fractional part with 1/2. We round up the fraction if it is equal to or greater than 1/2, and we round down if it is less than 1/2. Let us understand rounding off fractions to the nearest whole number using the following example.

Example: Round the given fractions to the nearest whole number:

b.) \(6 \dfrac{2}{5}\)

a.) We can round off a proper fraction to the nearest whole number by following the simple rule of comparing it with 1/2. Since 3/4 is greater than 1/2, it will be rounded off to 1.

b.) \(6 \dfrac{2}{5}\) is a mixed fraction. Here, we will keep the whole number part aside and compare the fractional part with 1/2. So, keeping 6 aside, we will check if 2/5 is greater than or less than 1/2. Since 2/5 is less than 1/2, we will round the given mixed fraction to 6.

c.) 21/5 is an improper fraction, so we will convert it to a mixed fraction. This will make it \(4 \dfrac{1}{5}\). Now, we will keep the whole number part aside and compare the fractional part with 1/2. So, keeping 4 aside, we will check if 1/5 is greater than or less than 1/2. Since 1/5 is less than 1/2, we will round the given fraction to 4.

How to Round Off Decimal Numbers?

A decimal number is a combination of a whole number part and a fractional part separated by a decimal point. Rounding decimal numbers works in the same way as we round whole numbers although we need to know the decimal place values of all the digits in the given number. This refers to the digits given before the decimal point as well as the digits given after the decimal point. Observe the decimal place value chart to understand this better.

We usually round decimal numbers to the nearest tenths, hundredths, thousandths, and so on, which represent the place values after the decimal point. However, sometimes we even need to round a decimal to the nearest whole number. In this case, we check the tenths digit. If it is equal to or more than 5, then the given number is rounded up, and if the tenths digit is less than 5 then the given number is rounded down.

Example 1: Round 5.62 to the nearest whole number.

Solution: Since we need to round this decimal to the nearest whole number, we will check the tenths digit. In this case, the tenths digit is 6, which is more than 5. So, the number will be rounded to 6. In other words, 5.62 ≈ 6

In the other cases, where we need to round decimals to the nearest tenths, hundredths, or thousandths, we need to remember the simple rule of marking the number up to which we are rounding and checking the number to its right. For example, when we round decimal numbers to the nearest hundredths, we need to check the thousandths place. Similarly, if we need to round decimal numbers to the nearest tenths, we need to check the hundredths place. If the number to be checked is less than 5, then the rounding number remains unchanged, and the following digits are replaced with 0. Whereas, if the number to be checked is 5 or more than 5, then the rounding number is increased by 1 and the following digits are changed to 0. Let us understand this with an example.

Example 2: Round 0.439 to the nearest hundredths.

Solution: In this case, the digit to the right of the hundredths place, that is, the thousandths place is 9, which is more than 5. So, we will add 1 to the digit in the hundredths place, that is, 3 + 1 = 4, and write 0 in the digits to the right. So, 0.439 will be rounded to 0.44

Note: It should be noted that when we round a decimal number to the nearest hundredth, the round decimal fraction is said to be correct to two places of decimal. In other words, if we are asked to round off a number to two decimal places, it means we need to round it to the nearest hundredths. Similarly, when we are asked to round off a number to one decimal place, it means we need to round it to the nearest tenths .

Tips on Rounding Numbers:

The following tips are helpful in solving questions related to rounding numbers.

• While rounding numbers, we always need to check the digit to the right of the rounding number. If it is less than 5, the rounding number remains the same and the following digits are changed to 0. If the digit to the right is equal to or more than 5, we increase the rounding digit by 1 and the following numbers are changed to 0.
• When we round decimal numbers, we usually come across terms like round to the nearest tenths, hundredths, thousandths, and so on.
• When we are asked to round off a number to one decimal place, it means we need to round it to the nearest tenths, similarly, when we are asked to round off a number up to two decimal places, it means we need to round it to the nearest hundredths.
• When the rounded number is increased, then the given number is said to be rounded up, whereas, if the rounded number is decreased, then it is said to be rounded down.

Related Topics

Check out the following links related to rounding numbers.

• What are Numbers?
• Number Line

Rounding Numbers Examples

Example 1: Round 321 to the nearest hundred, using the rules for rounding numbers.

While rounding numbers to the nearest hundred, we check the digit in the tens place. In this case, it is 2, which is less than 5. Therefore, this digit and all the digits to its right will change to 0 and the digit in the hundreds place will remain the same. Therefore, 321 is rounded to 300. This can be expressed as 321 ≈ 300.

Example 2: Using the rules of rounding numbers, round \(6 \dfrac{1}{5}\) to the nearest whole number.

A mixed fraction is made up of a whole number part and a fractional part. When we round off mixed fractions to a whole number, we compare the fractional part with 1/2. In this case, 6 is the whole number part and 1/5 is the fractional part. Now, we will keep the whole number part aside and compare the fractional part with 1/2. So, keeping 6 aside, we will check if 1/5 is greater than or less than 1/2. Since 1/5 is less than 1/2, we will round the given fraction to 6. Therefore \(6 \dfrac{1}{5}\) ≈ 6

go to slide go to slide

Book a Free Trial

Practice Questions

Faqs on rounding numbers, what is rounding numbers in math.

Rounding a number means converting a number to a simpler value such that its value remains close to what it was. Rounding numbers makes calculation simpler and converts figures to an approximate value which is easier to remember. For example, if the population of a town is 692,769, it can be rounded to 700,000, and it would be easier to remember an approximate figure of 700,000 rather than the real figure.

What are the Rules for Rounding Off Decimal Numbers?

There are some basic rules that need to be followed for rounding decimal numbers. They are similar to rounding the other numbers, however, we need to know the decimal place values of all the digits in the given number. This refers to the digits given before the decimal point as well as the digits given after the decimal point. In other words, we usually round decimal numbers to the nearest tenths, hundredths, thousandths, and so on, which represent the place values after the decimal point. Sometimes, we even round the decimal to the nearest whole number. In all these cases, we use the following rules.

For example, if we need to round 0.476 to the nearest tenths, it means we will check the digit to its right, which is the hundredths digit. In this case, it is 7 which is more than 5. Therefore, 0.476 will be rounded up to 0.5 to the nearest tenths.

What is 62 Rounded to the Nearest ten?

When 62 is rounded to the nearest 10, we need to check the digit in ones place. Here, it is 2, which is less than 5. So, 6 will remain the same, and 2 will change to 0. Therefore, 62 rounded to the nearest ten will be 60.

Where do we Use Rounding of Numbers in Real Life?

In real life, we usually round numbers whenever the exact value is not so important. For example, if we want to know the approximate amount that we spent in a grocery store, or the amount while estimating a budget, or while expressing larger figures like the population of a town. We estimate the amount to simpler numbers so that calculation becomes easier. For example, if we know that our monthly expenditure would be around $590, we can easily round the number to $600 which is a figure that is easier to remember.

How to Round Numbers to the Nearest Tenth?

If we need to round decimal numbers to the nearest tenth, we need to check the digit to the right of the digit on the tenths place, which is the hundredths place. If the number in the hundredths place is less than 5, then the rounding number remains unchanged, and the following digits are replaced with 0. Whereas, if the number to be checked is 5 or more than 5, then the rounding number is increased by 1 and the following digits are changed to 0. For example, to round 56.73 to the nearest tenth, we will check the digit in the hundredths place, which is 3 in this case. Since 3 is less than 5, 7 will remain the same and the following digits will become 0. So, 56.73 rounded to the nearest tenths will become 56.7

What is the Purpose of Rounding Numbers?

Rounding numbers means adjusting the digits of a number such that it gives an estimated result. Rounding a number gives an approximate value which is a simpler and a shorter representation of the given number. For example, if the population of a town is 498,821, it would be easier if it is expressed as 500,000. This helps in making calculations easier with a figure that is easy to remember and note. However, rounding of numbers is done in those cases where the exact value does not hold that much importance.

What is Rounding Numbers to the Nearest Ten?

When we round numbers to the nearest ten, we first mark the digit in the tens place. Then, we observe the 'ones' place, which lies to the right of the tens column. According to the rules, if the digit in the ones place is 5 or more than 5, we add 1 to the digit in the tens place, that is, we increase the tens place by 1 and write 0 in all the digits to the right. However, If the digit in the ones place is less than 5, we write 0 in the ones place and in all the places to its right, and the digit in the tens place remains the same. For example, if we need to round 389 to the nearest ten, we will check the digit in ones place. In this case, it is 9 which is more than 5. So, 8 will change to 9, and 389 will be rounded to 390.

How to Round Numbers to the Nearest 100?

In order to round numbers to the nearest hundred, we need to check the digit to its right, which is the tens place. For example, if we need to round 3270 to the nearest 100, we will check the tens place. In this case, it is 7, which means the digit in the hundreds place will be increased by 1, that is, 2 will become 3 and the remaining digits to its right will become zero. Therefore, 3270 will be rounded up to 3300.

How to Round Numbers to the Nearest Thousand?

When we round numbers to the nearest thousand, we check the digit in the hundreds place. If the digit in the hundreds place is 5 or more than 5, we increase the thousands place by 1 and write 0 in all the digits to the right. In case, if the digit in the hundreds place is less than 5, we write 0 in the hundreds place and in all the places to its right, while the digit in the thousands place remains as it is. For example, let us round 76431 to the nearest thousand. We will first check the digit in the hundreds place. In this case, it is 4, which is less than 5. So, 6 will remain as it is and all the digits to the right will become 0. Therefore, 76431 will be rounded to 76000.

Rounding – Definition with Examples

What do you mean by rounding off a number, example of rounding off from everyday life, how to round off different numbers, solved examples , practice problems, frequently asked questions.

Rounding off is nothing but estimation. Estimating the actual number to its nearby number is called rounding off. 

Recommended Games

When someone asks you the price of your book, you say 100 even if it is 98. This is giving an estimation after rounding off a number. This is how we apply the concept of rounding off in our everyday life. 

Recommended Worksheets

More Worksheets

Different numbers use different ‘rounding off’ rules. Let’s discuss them one by one.

Whole Numbers

Whole numbers are rounded off at different place values. 

Nearest Ten

Check the unit place digit:

• If the unit place digit is less than 5 then keep the tens place digit the same and put 0 at the unit place. 
• If the unit place is 5 or more than 5 then change the tens digit into its successor and put 0 at the unit place. 

Example: 

If we round off 15,493 to the nearest tens place then the answer will be 15,490. 

As the unit place is less than 5, the tens place digit will not change. 

Similarly, if we round off 12,359 to its nearest tens place then the answer will be 12,360.

As the unit place is more than 5, the tens place digit will change its successor. 

Nearest Hundred

Check the tens place digit:

• If the tens place is less than 5 then keep the hundred place digit the same and put 0 at the tens and unit place. 
• If the tens place is 5 or more than 5 then change the hundred digit into its successor and put 0 at the tens and unit place.

If we round off 15,443 to the nearest hundred places then the answer will be 15,400. As the tens place is less than 5, the hundred place digit will not change. 

Similarly, if we round off 12,359 to its nearest hundred places then the answer will be 12,400. 

As the tens place is 5, the hundred place digit will change to its successor. 

Nearest Thousand

Check the hundred place digit:

• If the hundred place digit is less than 5 then keep the thousand place digit the same and put 0 at the hundred, tens, and unit place. 
• If the hundred place digit is 5 or more than 5 then change the thousand place digit into its successor and put 0 at the hundred, tens, and unit place. 

If we round off 15,443 to the nearest thousand place digit then the answer will be 15,000. As the hundred place digit is less than 5, the thousand place digit will not change. 

Similarly, if we round off 12,659 to its nearest thousand place digit then the answer will be 13,000. 

As the hundred place digit is more than 5, the thousand place digit will change to its successor. 

Decimal Number

The concept is quite similar to the whole number with some minor but noteworthy changes. If the digit right to the place value you are rounding to is less than 5, round down. However, if it’s 5 or more than 5, round up.

Nearest Whole

5.9165 rounded to the nearest whole is 6.

As 5 is followed by 9 and 9 is greater than 5. So, round up.

Nearest Tenth

5.9165 rounded to the nearest tenth is 5.9

As 9 is followed by 1 and 1 is smaller than 5. So, round down.

Nearest Hundredth

5.9165 rounded to the nearest hundredth is 5.92.

As 1 is followed by 6 and 6 is greater than 5. So, round up.

Nearest thousandth

5.9165 rounded to the nearest thousandth is 5.917.

As 6 is followed by 5. So, round up.

Example 1. Round off the following numbers to the nearest ten:

Solution 1. 

• 5,499 rounded to the nearest ten is 5,500.

The unit place digit is more than 5 so add one to the tens place digit. 

•  3,453 rounded to the nearest ten is 3,450.

The unit place digit is less than 5 so the tens place digit will remain the same. 

• 4,405 rounded to the nearest ten is 4,410.

The unit place digit is 5 so add one to the tens place digit. 

Example 2. Round off the following numbers to the nearest hundredth.

Solution 2. 

• 2.656 rounded to the nearest hundredth is 2.66.

The digit next to the hundredth place digit is more than 5 so add 1 to the hundredth place digit. 

• 2.305 rounded to the nearest hundredth is 2.31.

The digit next to the hundredth place digit is 5 so add 1 to the hundredth place digit. 

• 3.234 rounded to the nearest hundredth is 3.23.

The digit next to the hundredth place digit is less than 5 so the hundredth place digit will remain the same. 

Example 3. Round off the following numbers to the nearest thousand. 

Solution 3.

• 44,590 rounded to the nearest thousand is 45,000.

The hundred place digit is 5 so add 1 to the thousand place digit. 

• 66,235 rounded to the nearest thousand is 66,000.

The hundred place digit is less than 5 so keep the thousand place digit the same as before.

Rounding off

Attend this Quiz & Test your knowledge.

A number rounded to the nearest 10 is 500. What could be the possible number?

Simplify the following after rounding off each number to the nearest hundred 45,789 + 23,848 + 66,321 – 34,213, match the numbers with their round off to the nearest tens..

Can we round off lengths and heights?

Yes. Heights and lengths can be rounded off.

What is 9,999 rounded off to the nearest hundred?

If we round off 9,999 to the nearest hundred, we will get 10,000.

Are round-off figures exact?

No. Round-off figures are not exact but are in proximity to the exact figure.

RELATED POSTS

• Row in Math
• Rounding To The Nearest Tens – Definition, Examples, FAQs
• Even Numbers and Odd Numbers – Properties, Examples
• Rounding Decimals – Definition with Examples
• Multiplying Decimals – Definition with Examples

Math & ELA | PreK To Grade 5

Kids see fun., you see real learning outcomes..

Make study-time fun with 14,000+ games & activities, 450+ lesson plans, and more—free forever.

Parents, Try for Free Teachers, Use for Free

Rounding Practice Questions

Click here for questions, click here for answers.

Also see: Error interval practice questions

GCSE Revision Cards

5-a-day Workbooks

Primary Study Cards

Privacy Policy

Terms and Conditions

Corbettmaths © 2012 – 2024

• Home   |  
• About   |  
• Contact Us   |  
• Privacy   |  
• Newsletter   |  
• Shop   |  
• 🔍 Search Site
• Easter Color By Number Sheets
• Printable Easter Dot to Dot
• Easter Worksheets for kids
• Kindergarten
• All Generated Sheets
• Place Value Generated Sheets
• Addition Generated Sheets
• Subtraction Generated Sheets
• Multiplication Generated Sheets
• Division Generated Sheets
• Money Generated Sheets
• Negative Numbers Generated Sheets
• Fraction Generated Sheets
• Place Value Zones
• Number Bonds
• Addition & Subtraction
• Times Tables
• Fraction & Percent Zones
• All Calculators
• Fraction Calculators
• Percent calculators
• Area & Volume Calculators
• Age Calculator
• Height Calculator
• Roman Numeral Calculator
• Coloring Pages
• Fun Math Sheets
• Math Puzzles
• Mental Math Sheets
• Online Times Tables
• Online Addition & Subtraction
• Math Grab Packs
• All Math Quizzes
• 1st Grade Quizzes
• 2nd Grade Quizzes
• 3rd Grade Quizzes
• 4th Grade Quizzes
• 5th Grade Quizzes
• 6th Grade Math Quizzes
• Place Value
• Rounding Numbers
• Comparing Numbers
• Number Lines
• Prime Numbers
• Negative Numbers
• Roman Numerals
• Subtraction
• Add & Subtract
• Multiplication
• Fraction Worksheets
• Learning Fractions
• Fraction Printables
• Percent Worksheets & Help
• All Geometry
• 2d Shapes Worksheets
• 3d Shapes Worksheets
• Shape Properties
• Geometry Cheat Sheets
• Printable Shapes
• Coordinates
• Measurement
• Math Conversion
• Statistics Worksheets
• Bar Graph Worksheets
• Venn Diagrams
• All Word Problems
• Finding all possibilities
• Logic Problems
• Ratio Word Problems
• All UK Maths Sheets
• Year 1 Maths Worksheets
• Year 2 Maths Worksheets
• Year 3 Maths Worksheets
• Year 4 Maths Worksheets
• Year 5 Maths Worksheets
• Year 6 Maths Worksheets
• All AU Maths Sheets
• Kindergarten Maths Australia
• Year 1 Maths Australia
• Year 2 Maths Australia
• Year 3 Maths Australia
• Year 4 Maths Australia
• Year 5 Maths Australia
• Meet the Sallies
• Certificates

Rounding Decimals Worksheet Challenges

Welcome to our Rounding Decimals Worksheet collection of Rounding Challenges. Here you will find a wide range of free printable math Worksheets, which will help your child learn to apply their rounding knowledge to solve a variety of rounding challenges involving decimals.

For full functionality of this site it is necessary to enable JavaScript.

Here are the instructions how to enable JavaScript in your web browser .

Rounding Decimals Worksheets

Here you will find a range of selection of printable rounding challenges to give your child practice and consolidation with their rounding work.

These sheets are carefully graded so that the easier sheets come first.

Each challenge consists of 4 clues and 8 possible answers, of which only one is correct.

Children have to look at the clues and use them to work out the correct answer.

These activities can be used individually with children working through the challenges on their own, but they are also great for partner work, and children discussing and sharing their ideas, and developing their mathematical language.

The activities are also a great way of extending more able mathematicians.

Each sheets comes with a separate printable answer sheet.

Using these sheets will help your child to:

• apply their rounding knowledge to solve problems;
• solve mathematical problems;
• develop children's vocabulary and understanding of the properties of numbers.

Rounding Decimals Challenges to the nearest whole

• Decimal Numbers Rounding Challenge 1
• Challenge 1 Answers
• PDF version
• Decimal Numbers Rounding Challenge 2
• Challenge 2 Answers

Rounding Decimals Challenge to the nearest whole / tenth

• Decimal Numbers Rounding Challenge 3
• Challenge 3 Answers
• Decimal Numbers Rounding Challenge 4
• Challenge 4 Answers

Rounding Decimals Challenges up to 2 decimal places

• Rounding Decimals Challenge 5
• Challenge 5 Answers
• Rounding Decimals Challenge 6
• Challenge 6 Answers

Looking for something easier?

The rounding challenges in this section involve rounding numbers to the nearest 10, 100 or 1000.

They are at a more basic level than those on this page, and do not involve decimals.

• Rounding Numbers Worksheet Challenges

More Recommended Math Worksheets

Take a look at some more of our worksheets similar to these.

How to Round whole numbers

• learn to round decimals to the nearest whole, tenth or 2 decimal places.

Each of the webpages below comes with rounding help as well as practice worksheets.

• Rounding Decimals to the nearest whole
• Rounding to the nearest tenth
• Rounding Decimal Places Sheets to 2dp

Decimal Place Value Worksheets

Here you will find a range of Free Printable Decimal Place Value Worksheets.

The following worksheets involve using and understanding decimal notation - tenths and hundredths.

• Understand decimals;
• Use place value notation with tenths and hundredths;

The free place value worksheets in this section support elementary math benchmarks.

• Decimal Place Value Worksheets to 2dp
• 5th Grade Place Value to 3dp

Online Rounding Practice Zone

In our Rounding Practice zone, you can practice rounding a range of numbers. You can round numbers to the nearest 10, 100 or even 1000. Want to round numbers to the nearest decimal place, you can do that too!

Select the numbers you want to practice with, and print out your results when you have finished.

You can also use the practice zone for benchmarking your performance, or using it with a group of children to gauge progress.

• Rounding Practice Zone

How to Print or Save these sheets 🖶

Need help with printing or saving? Follow these 3 steps to get your worksheets printed perfectly!

• How to Print support

Subscribe to Math Salamanders News

Sign up for our newsletter to get free math support delivered to your inbox each month. Plus, get a seasonal math grab pack included for free!

• Newsletter Signup

Return to Rounding Hub Page

Return from Rounding Decimals Worksheet Challenges to Math Salamanders Home Page

Math-Salamanders.com

The Math Salamanders hope you enjoy using these free printable Math worksheets and all our other Math games and resources.

We welcome any comments about our site or worksheets on the Facebook comments box at the bottom of every page.

New! Comments

TOP OF PAGE

© 2010-2024 Math Salamanders Limited. All Rights Reserved.

• Privacy Policy
• Copyright Policy

• International
• Education Jobs
• Schools directory
• Resources Education Jobs Schools directory News Search

Rounding reasoning & problem solving

Subject: Mathematics

Age range: 7-11

Resource type: Worksheet/Activity

Last updated

2 October 2016

• Share through email
• Share through twitter
• Share through linkedin
• Share through facebook
• Share through pinterest

Creative Commons "Sharealike"

Your rating is required to reflect your happiness.

It's good to leave some feedback.

Something went wrong, please try again later.

lorraivalentina

great activity.

Empty reply does not make any sense for the end user

Great thanks - really good to get my LA Yr5er thinking.

This is really good for your HA and as extension. Just what I needed

haixalo2021991

This is a great problem solving activity on problem solving, thanks

Report this resource to let us know if it violates our terms and conditions. Our customer service team will review your report and will be in touch.

Not quite what you were looking for? Search by keyword to find the right resource:

Grab my Math Problem-Solving Sampler Pack!

This handy download includes a variety of resources to help your students master word problems! You’ll find the ready-to-go Small Group Planner, the Problem-Solving Rounds Cheat Sheet, the printable Thinking Mat for any word problem, plus unique options for practice. Get it now when you sign up for free resources and teaching tips from Teacher Trap!

Problem Solving Rounds for Math Word Problems

In Word Problems Made Easy , I shared my favorite tips and tricks for helping students master math word problems. In this post, I’d like to take a closer look at one of the strategies I mentioned: Problem Solving Rounds. This powerful routine changed math instruction in my classroom forever!

Problem Solving Rounds are an important part of my math instruction. Almost every day, we take time to work through a math word problem together. In some units, this process becomes part of my daily math review, while in others the rounds are a key part of the unit itself.

NOTE: You can download a FREE printable version of this chart in my Word Problem Bundle Sampler Pack ! 

Round 1: Understand

The first round is all about helping students SLOW down and pay closer attention to the actual word problem.  In this round, we don’t discuss how we will solve the problem or the strategies that might work best, but instead focus on our understanding of what is happening in the problem.

I always ask students to first read the problem independently. I say, “Please read the problem twice and try to visualize what is happening.”  After a moment of silent reading time, I’ll invite students to share out important details from the problem.  

There are 29 monkeys eating bananas.

There are 18 monkeys eating bugs.

More monkeys are eating bananas than bugs.

Next, I ask if anyone noticed important clue words.

I noticed the phrase “how many more.”

And last, I ask students to turn to their neighbor and restate the question in their own words. I might also ask them to craft an Answer Statement.

We have to find out how many more monkeys are eating bananas.

We need to know the difference between monkeys eating bananas and monkeys eating bugs.

There are ___ more monkeys eating bananas than bugs.

Round 2: Plan

The rounds follow the same problem-solving process we follow on their Thinking Mat (Plan, Solve, Check), so the next step is to make a plan. I tell students to “Turn and Teach.” Their job is to explain to their partner the steps involved in solving the problem. During this round, students may not write or share the answer. The goal is to give step-by-step instructions. 

The partners may not agree, but should listen to each other’s ideas and discuss why different strategies do or don’t make sense.  This round is especially powerful for students who like to think aloud (think by talking) and for those who feel unsure about how to tackle the problem.

Round 3: Solve

Now, students can finally pick up their pencil and solve the problem. In this round, the class works independently to carry out the plan they discussed and solve the problem.  There is no talking! The goal is to give the class silent work time and challenge students to carry out the steps on their own.  For students who finish quickly, I encourage them to try solving another way.

Round 4: Check

The final round includes 3 important parts. First, I ask students to turn back to their partner and prove their thinking. Partners take turns showing each other their work, explaining their steps, and demonstrating how they know their answer is correct. This allows students to hear other ways of solving and other explanations of the steps.

Next, we do a Strategy Share and look at the correct answer. For this part, I select work from a few students and highlight specific strategies. For example, I might select a student who used a very efficient strategy and ask that student to explain their work to the class.  This is also a great time to highlight work from students who need to grow their confidence! 

Last, students go back to their work and do any Final Fix-Ups. This is their chance to rethink their work and make any needed changes.

Why This Works

Problem Solving Rounds are a powerful tool for encouraging thoughtful problem-solving and growing your students ability to think through tricky word problems. Because the routine matches the format of the Thinking Mat I use, students develop a habit of planning, solving, and checking any word problem they encounter.

You can download a FREE Problem-Solving Rounds Chart and Thinking Mat in my Word Problem Bundle Sampler Pack or any set from my Word Problem Solving Bundle .

The habits formed by regular use of Problem Solving Rounds and the Thinking Mat have helped my students become more confident and effective problem-solvers in all areas. I’ve seen gains not only with their ability to tackle tricky word problems, but also in their test-taking skills.

As always, I’d love to hear from you! What are your students struggling with most? What tips can you offer other teachers?

You might also like:

How to Fix Your Daily Math Review

Word Problems Made Easy

Leave a Comment Cancel Reply

Your email address will not be published. Required fields are marked *

Get in touch and learn more!

[email protected]

Click to follow on Instagram!

Subscribe for monthly freebies!

Get the Character Traits Printable!

Grab this resource now when you sign up for free resources and teaching tips from Teacher Trap!

Please check your email now to confirm! If you don't see it, check your Spam folder!

Get the Problem-Solving Sampler Pack!

WOOT early bird pricing ends on Monday, August 19th!

Something appears to not have loaded correctly.

Click to refresh .

Reading & Math for K-5

• Kindergarten
• Learning numbers
• Comparing numbers
• Place Value
• Roman numerals
• Subtraction
• Multiplication
• Order of operations
• Drills & practice
• Measurement
• Factoring & prime factors
• Proportions
• Shape & geometry
• Data & graphing
• Word problems
• Children's stories
• Leveled Stories
• Sentences & passages
• Context clues
• Cause & effect
• Compare & contrast
• Fact vs. fiction
• Fact vs. opinion
• Main idea & details
• Story elements
• Conclusions & inferences
• Sounds & phonics
• Words & vocabulary
• Reading comprehension
• Early writing
• Numbers & counting
• Simple math
• Social skills
• Other activities
• Dolch sight words
• Fry sight words
• Multiple meaning words
• Prefixes & suffixes
• Vocabulary cards
• Other parts of speech
• Punctuation
• Capitalization
• Narrative writing
• Opinion writing
• Informative writing
• Cursive alphabet
• Cursive letters
• Cursive letter joins
• Cursive words
• Cursive sentences
• Cursive passages
• Grammar & Writing

Breadcrumbs

• Place value & rounding

Download & Print Only $3.50

Place Value & Rounding for Grade 5

Place value worksheets.

Our grade 5 place value worksheets provide students practice in composing and decomposing whole and decimal numbers, as well as rounding to various digits.

Sample Grade 5 Place Value Worksheet

More place value & rounding worksheets

Explore all of our place value worksheets , from base ten blocks to 6 digit numbers in expanded form, and our rounding worksheets , ranging from rounding to the nearest 10 to rounding in the millions.

What is K5?

K5 Learning offers free worksheets , flashcards  and inexpensive  workbooks  for kids in kindergarten to grade 5. Become a member  to access additional content and skip ads.

Our members helped us give away millions of worksheets last year.

We provide free educational materials to parents and teachers in over 100 countries. If you can, please consider purchasing a membership ($24/year) to support our efforts.

Members skip ads and access exclusive features.

Learn about member benefits

This content is available to members only.

Join K5 to save time, skip ads and access more content. Learn More

• Forgot Password?

• Services & Software

iOS 18 Beta: Make Messages Do the Math for You

No need to switch back and forth between your Calculator app anymore.

• Apple software beta tester, "Helps make our computers and phones work!" - Zach's grandparents

Apple released the fourth public beta of iOS 18 on Aug. 12, about two months after the tech giant announced the software at its Worldwide Developers Conference in June. The betas bring a lot of new features to the iPhones of developers and beta testers, like more ways to customize your home and lock screens, as well as RCS messaging . And the operating system also lets you perform math problems right in your Messages app, too. 

Prior to iOS 18, if you wanted to figure out how to split a bill with your texting group from afar, you'd have to use your Calculator app or Spotlight and then switch back to Messages. With iOS 18 you can perform multi-step calculations in Messages -- as well as convert things like currency and temperature -- without switching apps.

Read more: Everything You Need to Know About iOS 18

However, iOS 18 is still in beta, and I recommend only downloading a beta on something other than your primary device. Betas can be buggy and cause short battery life, and it's best to keep those issues on a secondary device. I download and test betas on an old iPhone XR in order to keep those issues away from my primary phone, an iPhone 14 Pro. 

And remember, this beta isn't the final version of iOS 18, so more features could be available on your iPhone when Apple releases the software this fall.

How to solve math problems in Messages

In order to solve a math equation in Messages, type the problem into your text field, add the equals sign ( = ) and the solution will appear in the predictive text field over your keyboard. Tap the solution to add it to your text. 

Messages can solve simple equations -- like "2+2=" -- by typing them into the text field. The app can also solve equations that use more complex formulas, like the trigonometric functions of sine, cosine and tangent. You need to include the equals sign ( = ) at the end no matter what.

How to convert values in Messages

Converting values in Messages works similar to solving math problems in the app. Type the value into your text box with the appropriate value marker -- like F for Fahrenheit or lbs for pounds -- and then type the equal sign ( = ), and the predictive text field above your keyboard will show you the conversion. 

If you don't indicate what to convert to, predictive text will choose what to convert to. Don't worry -- it won't try to convert pounds to minutes. Messages will show conversions to other similar units, so Fahrenheit will convert to Celsius and pounds will convert to kilograms. 

You can choose what to convert to by typing something like "60hr to min=" and Messages will display the conversion in the predictive text field -- that's 3,900 minutes.

But these features are still in beta so they could be buggy. There will likely be more betas before the OS is released to the public this fall, so there's plenty of time for Apple to address any issues. As of now, there's no word on when Apple will release iOS 18 to the general public.

For more on iOS 18, here's my hands-on experience with the iOS 18 beta , how to ensure RCS messaging is enabled on your iPhone and our iOS 18 cheat sheet . 

Services and Software Guides

• Best iPhone VPN
• Best Free VPN
• Best Android VPN
• Best Mac VPN
• Best Mobile VPN
• Best VPN for Firestick
• Best VPN for Windows
• Fastest VPN
• Best Cheap VPN
• Best Password Manager
• Best Antivirus
• Best Identity Theft Protection
• Best LastPass Alternative
• Best Live TV Streaming Service
• Best Streaming Service
• Best Free TV Streaming Service
• Best Music Streaming Services
• Best Web Hosting
• Best Minecraft Server Hosting
• Best Website Builder
• Best Dating Sites
• Best Language Learning Apps
• Best Weather App
• Best Stargazing Apps
• Best Cloud Storage
• Best Resume Writing Services
• New Coverage on Operating Systems

Skip to Content

Current Students

Interested in more? Search Courses

• Search Input Submit Search

DU Professor Helps Solve Famous 70-Year-Old Math Problem

Jordyn reiland.

[email protected]

Assistant Professor Mandi Schaeffer Fry is the first faculty member to be published in the Annals of Mathematics since the 1880s.

University of Kaiserslautern Professor Gunter Malle, University of Denver Assistant Professor Mandi Schaeffer Fry and University of Valencia Professor Gabriel Navarro pose for a photo after announcing their theorem in Oberwolfach, Germany.

Whether it be flying trapeze, participating in competitive weightlifting or solving math problems that have confounded academics for decades, Mandi Schaeffer Fry enjoys chasing the next adventure.

Schaeffer Fry, who joined the University of Denver’s Department of Mathematics in the fall of 2023, will be the first faculty member since the 1880s to be published in the Annals of Mathematics , widely seen as the industry’s most prestigious journal.

In 2022, Schaeffer Fry helped complete a problem that dates to 1955—mathematician Richard Brauer’s Height Zero Conjecture.

“Maybe one of the most challenging parts, other than the math itself, was the knowledge of the weight that this would have on the field,” Schaeffer Fry says. “If you’re going to make an announcement like this, you have to be darn sure that it’s absolutely correct.”

Over the years, number crunchers have worked on the problem at universities across the globe, and some found partial solutions; however, the problem was not completed until now.

“Mandi’s accomplishment is exciting. Solving Brauer's Height Zero Conjecture is remarkable,” Mathematics Department Chair Alvaro Arias says. 

The work is also a testament to DU’s achievement as a Research 1 (R1) institution.

Fry and her collaborators—University of Kaiserslautern Professor Gunter Malle, University of Valencia Professor Gabriel Navarro and Rutgers University Professor Pham Huu Tiep—worked around the clock over the course of three months in eight-hour shifts during the summer of 2022 to find a solution.

In April, that work was accepted for publication in the Annals of Mathematics.

'Brauer's Height Zero Conjecture (BHZ) was the first conjecture leading to the part of my field studying 'local-global' problems in the representation theory of finite groups, which seek to relate properties of groups with properties of certain nice smaller subgroups, letting us 'zoom in' on the group using just a specific prime number and simplify things," Schaeffer Fry says. 

"The BHZ gives us a way to tell from the character table of a group (a table of data that encodes lots, but not all, information about the group) whether or not certain of these subgroups, called defect groups, have the commutativity property," she adds.

This paper was especially meaningful to Schaeffer Fry as she had always wanted to work with Malle, Tiep and Navarro as they have been her primary mentors. Tiep was her PhD advisor and this was the first time they had worked together since then.

Fry believes she has solidified her place in the field and knows she’ll likely never top this accomplishment, but she’s always looking for the next adventure—whether that’s in or out of the classroom.

Flying high and pumping iron

When Schaeffer Fry isn’t on DU’s campus working with students or conducting research, you can find her flying trapeze and competitive weightlifting.

Schaeffer Fry became involved in competitive weightlifting during graduate school, and, in the last year of her PhD at the University of Arizona, she defended her dissertation one day and got on a plane and competed at the national level for “university-aged” athletes—which included Olympians.

While she now lifts weights more casually, Schaeffer Fry competed last September in an over-35 competition and qualified for the USA Weightlifting Masters National Championships.

It was a “field trip” during a conference in Berkeley, California, in 2018 that led Fry to become enamored with flying trapeze.

In fact, she enjoyed it so much she signed up to be a member of Imperial Flyers, an amateur flying trapeze cooperative located in Westminster. Once she found out about the sport, her previous experience as a gymnast made it a natural fit.

Not only is she working on her own intermediate tricks, she’s also a “teaching assistant” at Fly Mile High, the state’s only flying trapeze and aerial fitness school.

“It’s exhilarating; it’s gotten me a bit over my fear of heights,” she says.

Related Articles

A Geology Expert’s Guide to Colorado’s Coolest Rock Formations

Research to Watch

Storytelling, Shaving Cream and Slime: Why Students Love Professor Nancy Sasaki

• Departments and Units
• Majors and Minors
• LSA Course Guide
• LSA Gateway

Search: {{$root.lsaSearchQuery.q}}, Page {{$root.page}}

• Mathematics
• Centers & Outreach
• Seminars, Colloquia & Lectures
• News & Events
• Diversity & Climate
• Undergraduates
• Alumni & Friends

• Undergraduate Math Courses
• Research and Career Opportunities
• Frequently Asked Questions
• Major and Minor Programs
• Awards, Scholarships, and Prizes
• Extracurricular Activities
• Transfer Credit
• Student Spotlight
• Students On the Job Market - AIM & Math
• Awards & Fellowships
• Recent Ph.D. Recipients
• Student Spotlight - AIM & Math
• Student Handbook - AIM & Math
• Thesis Defense Schedule
• Newsletters
• Giving to Mathematics
• Algebra and Algebraic Geometry
• Combinatorics
• Financial and Actuarial Mathematics
• Mathematical Biology
• Number Theory
• Research Training Grant
• Computer Science
• Geometry & Topology
• Mathematical Physics
• Probability Theory
• Named Postdoctoral Fellows
• Applied Mathematics
• Differential Equations
• Logic and Foundations
• Mathematics Education
• Scientific Computing

Unified continuous-time q-learning for mean-field game and mean-field control problems

• Information For
• Prospective Students
• Current Students
• Faculty and Staff
• Alumni and Friends
• More about LSA
• How Do I Apply?
• LSA Magazine
• Student Resources
• Academic Advising
• Global Studies
• LSA Opportunity Hub
• Social Media
• Update Contact Info
• Privacy Statement
• Report Feedback

Or search by topic

Number and algebra.

• Place value and the number system
• Fractions, decimals, percentages, ratio and proportion
• Calculations and numerical methods
• Algebraic expressions, equations and formulae
• Coordinates, functions and graphs
• Patterns, sequences and structure
• Properties of numbers

Geometry and measure

• 3D geometry, shape and space
• Transformations and constructions
• Vectors and matrices
• Measuring and calculating with units
• Pythagoras and trigonometry
• Angles, polygons, and geometrical proof

Probability and statistics

• Handling, processing and representing data
• Probability (spec_group)

Working mathematically

• Thinking mathematically
• Mathematical mindsets

Advanced mathematics

• Decision mathematics and combinatorics
• Advanced probability and statistics

For younger learners

• Early years foundation stage

Cover the Camel

Can you cover the picture of the camel with the two differently shaped pieces?

Use the interactive below to try out your ideas. You can drag a piece into place and you can turn (or rotate) a piece by clicking on it. Alternatively, you may like to print off and cut out the camel and pieces from these sheets .

What are you thinking about as you try to complete the picture? What 'top tips' might you give someone else?

This activity originally featured in the hands-on Brain Buster Maths Boxes, developed by members of the NRICH Team and produced by BEAM. These resources are out of print but can still be found on Amazon. 

If you are using the interactive, you can choose to see pieces which are already rotated. Click on the Settings menu (the purple cog in the top right-hand corner) and choose that option. Where might be a good place to start? Is there anywhere else you can put a piece straight-away? How about trying to put in pieces from one of these starting points, filling gaps as you go along?

You sent in a range of different ways of solving this problem, but there were some common themes. Nina wrote:

Here is Nina's completed solution:

Jazzy described how she filled the camel in:

Sophie sent us a picture of her completed camel which is filled in a different way compared with Nina's:

Well done all of you.

Why do this problem?

This problem is a lovely context in which children can develop their ability to visualise. Visualisation is required in two ways. Firstly, children will realise that planning ahead is useful, so as not to leave impossible spaces. Secondly, in the default version of the interactive, they must try to turn each piece in their 'mind's eye' to decide which is needed for a particular gap.  

Possible approach

You could introduce this task by showing the interactive projected onto the screen or whiteboard. Invite learners to talk about what they notice, and use their observations to explain the aim of the activity. In pairs, learners can have a go either using the interactive on a tablet/computer, or you can give them print outs of these  photocopiable sheets . (The image of the camel is on the first sheet and the ten pieces to fit into it on the second sheet.)

Give them time to begin to have a go at the task, observing how they get started and listening to their conversations. You may wish to draw everyone together for a mini plenary at a suitable opportunity. This could give some pairs the chance to articulate their thinking and to explain what they are attending to as they try to 'cover the camel'. Draw out the idea of visualising and don't be afraid to give it that label. In this task, visualising might be used to plan ahead, but also to picture what a piece will look like once it has been rotated and is placed in position. 

Having given everyone more time to try to complete the picture, a final plenary might involve looking at all the covered camels. Has every pair completed it in the same way? Is there more than one solution?

Key questions

Where might be a good place to start? Why? Is there anywhere else you can put a piece straight-away? If you put that piece there, will you be able to fit another one in easily? Have you tried turning the piece round? Have you tried turning the piece over so it's the other way up? Have you got any spaces that you can't fill? Have you counted the number of squares in the gap?

Possible extension

Learners could make their own designs on squared paper using these shapes.

Possible support

You could partially complete the camel yourself, and then ask learners to fill in the rest independently. If using the interactive, learners could click on the Settings menu (purple cog) and select the version which includes pieces that are already rotated. This means that they do not have to visualise the rotations, but will still need to use visualisation to decide how to place the pieces.