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 communication—19.87 becomes 'about 20'.

Read the full concept explanation →

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 trades precision for simplicity; look at the next digit to decide.

Common stuck point: The 'round 5 up' rule: when the deciding digit is exactly 5, round up—e.g., 2.45 rounded to tenths is 2.5.

Sense of Study hint: Underline the digit you are rounding to, then look one place to the right: if that digit is 5 or more, round up; otherwise keep it.

Worked Examples

Example 1

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

Solution

  1. 1
    Identify the target place and look at the digit immediately to its right.
  2. 2
    (a) Nearest hundred: The hundreds digit is 7; look at the tens digit: 3 < 5, so round down (keep hundreds digit as 7). 4{,}736.482 \approx 4{,}700.
  3. 3
    (b) Nearest tenth: The tenths digit is 4; look at the hundredths digit: 8 \geq 5, so round up. 4{,}736.482 \approx 4{,}736.5.

Answer

(a) 4{,}700; (b) 4{,}736.5
Rounding uses the digit immediately to the right of the target place: if it is 5 or more, increase the target digit by 1; if it is less than 5, leave the target digit unchanged. All digits to the right then become zero (or are dropped for decimals).

Example 2

medium
Round \pi \approx 3.14159265\ldots to 4 significant figures. Then round 0.0038472 to 3 significant figures.

Practice Problems

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

Example 1

easy
Round 8.965 to the nearest hundredth. Then round -3.45 to the nearest tenth.

Example 2

medium
A measurement is given as 5.28 m. Round to the nearest metre and estimate the percent error introduced.
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Background Knowledge

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

place value