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Rounding

FoundationChallengeAQAEdexcelOCR

Rounding is a key number topic at GCSE Maths. This Foundation worksheet gives you exam-style questions on rounding to decimal places and significant figures, with a full mark scheme so you can check every method mark. Suitable for AQA, Edexcel and OCR. Download the free PDF and answers below. Look at the next digit: 5 or more rounds up, 4 or less rounds down.

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Topic overview

Rounding replaces a number with a simpler one that is close enough for the purpose. You may be asked to round to a given number of decimal places, to a number of significant figures, or to the nearest ten, hundred or thousand.

The method is always the same. Find the digit in the place you are rounding to, then look at the digit immediately to its right. If that next digit is 5 or more, round up. If it is 4 or less, leave the digit as it is. Everything after the rounding position is then removed or replaced by zeros.

Rounding appears far beyond number questions. Almost every calculation topic asks for an answer to a sensible degree of accuracy, and marks are routinely lost for giving a long decimal where a rounded value was expected.

Revision notes

Rounding to decimal places

Decimal places are counted after the decimal point. To round to 2 decimal places, keep two digits after the point and look at the third to decide.

For \(3.7482\) rounded to 2 d.p., the second decimal is \(4\) and the next digit is \(8\), so you round up to \(3.75\). Zeros at the end still count as decimal places, so \(2.897\) to 2 d.p. is \(2.90\), not \(2.9\).

Rounding to significant figures

Significant figures are counted from the first non-zero digit, wherever it appears. In \(0.00427\) the first significant figure is the \(4\), so to 2 s.f. this is \(0.0043\).

With large numbers you must keep the place value. Rounding \(38\,600\) to 1 s.f. gives \(40\,000\), not \(4\) — the zeros hold the number in the right place.

Rounding up through a nine

When the digit you are rounding is a \(9\) and it rounds up, it becomes \(0\) and the digit to its left increases by one.

So \(4.97\) to 1 d.p. is \(5.0\), and \(199\) to the nearest ten is \(200\). Work leftwards until no further carrying is needed.

Key points

  • Look only at the digit immediately to the right of the rounding position.
  • 5 or more rounds up; 4 or less rounds down.
  • Decimal places are counted after the decimal point.
  • Significant figures start at the first non-zero digit.
  • Keep trailing zeros where they hold place value, such as \(40\,000\).
  • A 9 that rounds up becomes 0 and carries into the digit on its left.

Worked examples

Example 1

Round \(7.3649\) to 2 decimal places.

Working

\[7.3649\]identify the second decimal place, which is the 6
\[\text{next digit} = 4\]look at the digit immediately to its right
\[7.36\]4 is less than 5, so the 6 stays as it is

Example 2

Round \(0.005192\) to 2 significant figures.

Working

\[0.005192\]the first significant figure is the 5, so the second is the 1
\[\text{next digit} = 9\]look at the digit to the right of the 1
\[0.0052\]9 is 5 or more, so the 1 rounds up to 2

Example 3

Round \(48\,962\) to 1 significant figure.

Working

\[48\,962\]the first significant figure is the 4, in the ten thousands column
\[\text{next digit} = 8\]look at the digit to its right
\[50\,000\]8 rounds the 4 up to 5, and the zeros hold the place value

Common mistakes

  • Writing 0.0043 as 0.004 when asked for 2 significant figures.

    Leading zeros are not significant, so counting starts at the first non-zero digit, not at the decimal point.

  • Dropping a trailing zero, such as writing 2.9 instead of 2.90.

    If the question asks for 2 decimal places, both decimal places must be shown, even when the last one is a zero.

  • Rounding 38 600 to 1 s.f. and writing 4.

    The zeros are needed to keep the number the right size. The answer is 40 000.

  • Rounding the digits one at a time from the right.

    Rounding 4.446 to 1 d.p. by first making it 4.45 and then 4.5 is wrong. Look only at the digit immediately after the rounding position, giving 4.4.

Exam tips

  • Read whether the question wants decimal places or significant figures — they often give different answers.
  • Round only at the very end of a calculation, using unrounded values in the working.
  • If no accuracy is specified, 3 significant figures is normally accepted.
  • Check your rounded answer is sensible next to the original number.

Key terms

Decimal place
A digit position after the decimal point.
Significant figure
A digit that contributes to the accuracy of a number, counted from the first non-zero digit.
Rounding up
Increasing the rounding digit by one because the next digit is 5 or more.
Degree of accuracy
How precisely an answer is given, such as to 2 d.p. or 3 s.f.

Related topics

Written and reviewed against the current AQA, Edexcel and OCR specifications. Spotted an error? Let us know.