Rounding Decimals

Rounding asks which mark a number is closer to. It is a question about distance.

Find the two neighbours first

To round 3.47 to tenths, notice it sits between 3.4 and 3.5.

Then decide

3.47 is past halfway, so it is nearer 3.5.

Exactly halfway

A number landing exactly on the midpoint rounds up. That is a convention, agreed so everyone matches.

Same question as always

Rounding 3.472 to the nearest hundredth means asking whether it is closer to 3.47 or 3.48. The halfway point is 3.475, and 3.472 is below it, so the answer is 3.47. The number line reasoning is identical to whole-number rounding.

The deciding digit

Look at the digit immediately right of the place you are rounding to. Here that is the 2 in the thousandths, which is below 5, so round down. Digits further right cannot change the outcome — 3.4749999 still rounds to 3.47.

Digits to the right are dropped, not zeroed

Rounding 3.472 to hundredths gives 3.47, not 3.470 — though writing 3.470 is not wrong, just unnecessary. This differs from whole numbers, where the places to the right must be filled with zeros to preserve size. Decimal places to the right of the last digit contribute nothing.

Why rounding decimals matters

Money rounds to hundredths, measurements round to whatever the instrument can resolve, and calculators produce more digits than any real measurement justifies. Reporting 3.4718294 metres when your ruler reads to centimetres claims a precision you do not have.