Lessons · Teaching · comparing, ordering and rounding

Rounding is choosing which of two numbers you are nearer to

Rounding a number to a place means replacing it with the nearest number that has zeros after that place. Look at the digit immediately to the right of the place you are rounding to: 5 or more rounds up, 4 or less stays. The digits after it all become zero.

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What it is for

Rounding is the only arithmetic most adults do in a shop, and it is also the skill that catches a wrong answer. A pupil who divides 812 by 4 and gets 23 has not noticed that 800 divided by 4 is 200. Estimation is not a lesser form of arithmetic. It is the check that tells you the exact answer is wrong.

How to think about it

Underline the place you are rounding to. Look only at the single digit to its right and ignore everything further right. Decide up or stay, then zero out everything after the underlined place. Say the two candidates out loud first, so the answer is a choice between two numbers rather than a rule applied blind.

Worked example

Round 3,472 to the nearest hundred: the candidates are 3,400 and 3,500

Naming both first is what stops the rule being applied with no meaning.

The digit right of the hundreds is 7, so round up: 3,500

Seven tens is more than half of a hundred, so 3,472 is nearer 3,500.

Round 0.248 to the nearest tenth: candidates 0.2 and 0.3, next digit is 4, so 0.2

Only the hundredths digit decides. The 8 after it does not get a vote.

Estimate 812 divided by 4 as 800 divided by 4, which is about 200

Now an answer of 23 is visibly wrong before it is checked.

Your turn

Name the only digit that decides whether a number rounds up.

The digit immediately to the  of the rounding place decides

The trap

Rounding twice. 0.248 to the nearest tenth is 0.2, not 0.3. Rounding to hundredths first gives 0.25, and rounding that again gives 0.3, which is a different and wrong answer. Round once, from the original number.

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