Rounding Examples in Math

Start with the recap, study the fully worked examples, then use the practice problems to check your understanding of Rounding.

This page combines explanation, solved examples, and follow-up practice so you can move from recognition to confident problem-solving in Math.

Concept Recap

Replacing a number with a nearby simpler approximation at a specified place value, using the digit to the right to decide.

Simplifying for easier calculation or communicationβ€”\$19.87 becomes 'about \$20'.

Read the full concept explanation β†’

How to Use These Examples

  • Read the first worked example with the solution open so the structure is clear.
  • Try the practice problems before revealing each solution.
  • Use the related concepts and background knowledge badges if you feel stuck.

What to Focus On

Core idea: Rounding replaces a number with the closest simpler value at a named place, deciding by the digit just to the right.

Common stuck point: The procedure for rounding is the easy part; the trap is looking at the wrong digit. Asking "Is there a named place value to snap to, and one digit to its right deciding the direction?" first is what keeps a correct-looking calculation from being attached to the wrong concept.

Sense of Study hint: Ask: Is there a named place value to snap to, and one digit to its right deciding the direction?

Worked Examples

Example 1

easy
Round 4,736.4824{,}736.482 to (a) the nearest hundred, (b) the nearest tenth.

Answer

(a) 4,7004{,}700; (b) 4,736.54{,}736.5

First step

1
Identify the target place and look at the digit immediately to its right.

Full solution

  1. 2
    (a) Nearest hundred: The hundreds digit is 77; look at the tens digit: 3<53 < 5, so round down (keep hundreds digit as 77). 4,736.482β‰ˆ4,7004{,}736.482 \approx 4{,}700.
  2. 3
    (b) Nearest tenth: The tenths digit is 44; look at the hundredths digit: 8β‰₯58 \geq 5, so round up. 4,736.482β‰ˆ4,736.54{,}736.482 \approx 4{,}736.5.
Rounding uses the digit immediately to the right of the target place: if it is 55 or more, increase the target digit by 11; if it is less than 55, leave the target digit unchanged. All digits to the right then become zero (or are dropped for decimals).

Example 2

medium
Round Ο€β‰ˆ3.14159265…\pi \approx 3.14159265\ldots to 44 significant figures. Then round 0.00384720.0038472 to 33 significant figures.

Example 3

medium
Round 234,567234{,}567 to (a) the nearest thousand, (b) the nearest ten thousand.

Example 4

medium
Round 0.045670.04567 to (a) 22 decimal places, (b) 33 decimal places, (c) 33 significant figures.

Example 5

medium
Use rounding to estimate 79Γ—4179 \times 41. Then compute the exact product.

Example 6

hard
A measurement is 12.34512.345. Round to (a) 22 decimal places using round-half-up; (b) 22 decimal places using banker's rounding (round-half-to-even).

Example 7

hard
A bag weighs 2.862.86 kg. Round to the nearest 0.50.5 kg.

Example 8

hard
A student rounds 3.141593.14159 to 22 decimal places and gets 3.143.14, then rounds 3.143.14 to 11 decimal place and gets 3.13.1. Now they round 3.141593.14159 directly to 11 decimal place β€” what do they get, and why might these differ?

Example 9

challenge
A statistician must round each of 0.5,1.5,2.5,3.50.5, 1.5, 2.5, 3.5 to the nearest whole number. Compare the totals using round-half-up vs round-half-to-even.

Practice Problems

Try these problems on your own first, then open the solution to compare your method.

Example 1

easy
Round 8.9658.965 to the nearest hundredth. Then round βˆ’3.45-3.45 to the nearest tenth.

Example 2

medium
A measurement is given as 5.285.28 m. Round to the nearest metre and estimate the percent error introduced.

Example 3

easy
Round 4747 to the nearest ten.

Example 4

easy
Round 8383 to the nearest ten.

Example 5

easy
Round 6565 to the nearest ten.

Example 6

easy
Round 342342 to the nearest hundred.

Example 7

easy
Round 7.87.8 to the nearest whole number.

Example 8

easy
Round 3.141593.14159 to the nearest hundredth.

Example 9

easy
Round 295295 to the nearest ten.

Example 10

easy
Estimate 38+5138 + 51 by rounding each to the nearest ten.

Example 11

medium
Round 2,7482{,}748 to the nearest thousand.

Example 12

medium
Estimate 612Γ—19612 \times 19 by rounding.

Example 13

medium
Round 0.04560.0456 to the nearest thousandth.

Example 14

medium
A bill is $23.47\$23.47. Round to the nearest dollar.

Example 15

medium
Round 9,9999{,}999 to the nearest hundred.

Example 16

medium
About how much is 19Γ—2119 \times 21? Estimate, then compare to exact.

Example 17

medium
Round 4,5674{,}567 to two significant figures.

Example 18

medium
A number rounds to 5050 when rounded to the nearest ten. What is the range of possible values (whole numbers)?

Example 19

medium
Round 0.4990.499 to the nearest whole number.

Example 20

challenge
xx rounds to 3.53.5 at the nearest tenth. What is the range of xx?

Example 21

challenge
Why can rounding twice give a wrong answer? Round 2.452.45 to the nearest tenth, then to the nearest whole β€” vs rounding 2.452.45 directly to the nearest whole.

Example 22

challenge
Three numbers each round to 1010 (nearest ten). What is the maximum possible value of their sum, using whole numbers?

Example 23

easy
Round 7474 to the nearest ten.

Example 24

easy
Round 158158 to the nearest hundred.

Example 25

easy
Round 6.496.49 to the nearest tenth.

Example 26

easy
Round 0.08340.0834 to the nearest hundredth.

Example 27

easy
Round 4.054.05 to the nearest tenth (round half up).

Example 28

medium
Round βˆ’3.27-3.27 to the nearest tenth.

Example 29

medium
Estimate 487+312487 + 312 by rounding each to the nearest hundred, then compare to the exact answer.

Example 30

medium
A grocery total is \$14.376. Round to the nearest cent.

Example 31

medium
A car odometer shows 48,62748{,}627 km. Round to the nearest thousand.

Example 32

medium
Round 2.718282.71828 to (a) the nearest tenth, (b) the nearest thousandth.

Example 33

hard
Round 0.499990.49999 to the nearest whole number, then to the nearest tenth.

Example 34

hard
A clothing store rounds prices up to the next $5\$5. A jacket priced $47.30 will be displayed at what price?

Example 35

hard
A class of 3434 students must be split into groups of 66. Round up to find the minimum number of groups.
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Background Knowledge

These ideas may be useful before you work through the harder examples.

place value