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Rounding Decimals

In one line: Rounding a decimal means swapping it for a simpler nearby number by looking only at the digit just after the place you are rounding to: if that digit is 5 or more, round up; if it is 4 or less, keep the digit the same.

Why it works

We round decimals all the time to make numbers easier to use, such as money to the nearest penny or cent, a height to the nearest centimetre, or a calculator answer that goes on for many digits. Rounding also helps children estimate and check whether an answer is sensible. A decimal place is a position after the decimal point: the first is tenths, the second is hundredths and the third is thousandths.

Think of it like: Imagine walking along a path with signposts every 0.1 metres, at 3.6, 3.7, 3.8 and so on. You are standing somewhere between two signposts and must walk to the closest one. If you are at 3.64, the 3.6 signpost is closer, so you go back to it. If you are at 3.67, the 3.7 signpost is closer, so you go forward. Rounding just means finding your nearest signpost. (Where this breaks: The path picture breaks when you are exactly halfway, for example at 3.65. Both signposts are the same distance away, so 'go to the closest' does not give an answer. Mathematicians agreed on a rule for this case: a 5 always rounds up, so 3.65 becomes 3.7.)

Worked example

Round 12.6481 to 2 decimal places.

  1. Two decimal places means we keep the hundredths digit. In 12.6481, the hundredths digit is 4.
  2. Look at the very next digit only (the thousandths digit). It is 8.
  3. 8 is 5 or more, so round up: the 4 becomes 5.
  4. Remove every digit after the hundredths place. The digits before it (12.6) stay the same.

Answer: 12.6481 rounded to 2 decimal places is 12.65.

Common mistakes

  • Rounding in stages, for example 2.346 → 2.35 → 2.4, gives the wrong answer; look only at the one digit right after your rounding place, so 2.346 to 1 decimal place is 2.3.
  • Dropping the zero, as in writing 4.96 rounded to 1 decimal place as 5, hides how accurate the answer is; write 5.0 so it still shows one decimal place.
  • Changing the digit when the next digit is 4 or less, for example rounding 7.82 to 7.9, is wrong; with 4 or less the digit stays the same, so the answer is 7.8.
  • Forgetting to carry when a 9 rounds up, for example writing 2.997 as 2.9100, is wrong; a 9 that rounds up becomes 0 and adds 1 to the digit on its left, giving 3.00.

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Round 5.73 to the nearest whole number.

Questions parents ask

What year do kids learn rounding decimals?

In the UK, children usually start in Year 5, rounding to the nearest whole number and to 1 decimal place, then extend it in Year 6. In Australia it is typically covered around Years 6–7, and in the US it is a Grade 5 skill. It is then used throughout secondary school.

How can I help my child with rounding decimals at home?

Use real prices and measurements: ask your child to round a shopping total to the nearest pound or dollar, or a height to the nearest centimetre. Encourage them to underline the digit they are keeping and circle the one digit after it before deciding. Short, regular practice works better than long sessions.

Why does 5 round up instead of down?

A number ending in exactly 5 is halfway between two options, so neither is closer. Rounding up on a 5 is simply the agreed rule everyone uses, so that answers are consistent. Your child may later meet other rules in science or computing, but rounding 5 up is the standard school method.

What is the difference between rounding and truncating?

Truncating means just chopping off digits without checking the next one, so 3.78 becomes 3.7. Rounding checks the next digit first, so 3.78 to 1 decimal place becomes 3.8. Many children truncate by accident, so it is worth asking them to always look at the next digit.