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Arithmetic with Decimals

FoundationChallengeAQAEdexcelOCR

This free Foundation GCSE Maths worksheet on arithmetic with decimals helps you revise calculating with decimals. Questions build from straightforward to exam standard, with full worked answers in the mark scheme — ideal for revision or homework. Suitable for AQA, Edexcel and OCR. When multiplying decimals, count the total number of decimal places in the question.

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These worksheets and mark schemes are original, written for Virtus Academy and checked against the current AQA, Edexcel and OCR specifications. Every worksheet comes with a full mark scheme.

Foundation

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Stretch yourself beyond the basics.

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Topic overview

Arithmetic with decimals uses the same methods as whole numbers, with one extra consideration: where the decimal point goes.

For addition and subtraction, align the decimal points vertically and pad with trailing zeros so every column is filled. The point in the answer sits directly below those in the question.

Multiplication and division work differently. For multiplication, ignore the points, multiply as whole numbers, then count the total decimal places in the question and place the point that many from the right. For division, scale both numbers until the divisor is a whole number.

Revision notes

Adding and subtracting

Line up the decimal points, pad with zeros, then add or subtract as usual.

For \(6.4 + 12.75\), write \(6.40\) above \(12.75\) so the columns match, giving \(19.15\).

Multiplying

Ignore the decimal points and multiply as whole numbers. Count the decimal places in both original numbers, and put that many in the answer.

For \(0.4 \times 0.03\): \(4 \times 3 = 12\), and there are three decimal places in total, so the answer is \(0.012\).

Dividing

Multiply both numbers by the same power of ten until the divisor is whole, then divide normally.

For \(3.6 \div 0.4\), multiply both by \(10\) to get \(36 \div 4 = 9\). Scaling both equally leaves the answer unchanged.

Key points

  • Align decimal points when adding or subtracting.
  • Pad with trailing zeros so columns match.
  • For multiplication, ignore the points and multiply as whole numbers.
  • Count total decimal places to place the point.
  • For division, scale both numbers so the divisor is whole.
  • Estimate first to check the answer is sensible.

Worked examples

Example 1

Work out \(8.6 + 3.47\).

Working

\[8.60 + 3.47\]pad so both have two decimal places
\[= 12.07\]add with the decimal points aligned

Example 2

Work out \(0.5 \times 0.06\).

Working

\[5 \times 6 = 30\]ignore the points and multiply as whole numbers
\[\text{3 decimal places in total}\]count the places in 0.5 and 0.06
\[= 0.03\]place the point three from the right and simplify

Example 3

Work out \(7.2 \div 0.9\).

Working

\[72 \div 9\]multiply both numbers by 10 so the divisor is whole
\[= 8\]carry out the division

Common mistakes

  • Lining numbers up on the right when adding.

    With decimals of different lengths this misaligns the columns. Align the points instead.

  • Miscounting decimal places in multiplication.

    0.4 × 0.03 has three decimal places, giving 0.012, not 0.12.

  • Scaling only the divisor.

    Both numbers must be multiplied by the same power of ten, or the answer changes.

  • Not estimating.

    A quick estimate catches a misplaced decimal point immediately.

Exam tips

  • Pad with trailing zeros before adding or subtracting.
  • Count the decimal places in the question, not in your working.
  • Scale both numbers before dividing.
  • Estimate the answer first as a check on the decimal point.

Key terms

Decimal place
A digit position after the decimal point.
Divisor
The number you are dividing by.
Pad
To add trailing zeros so numbers have equal decimal places.
Estimate
An approximate answer used as a check.

Related topics

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