N5NumberFoundation

Decimals

Decimals are just another way of writing fractions with denominators of 10, 100, 1000 and so on. The methods are like whole numbers — you just have to keep track of the decimal point.

30 min Video by GCSE Maths AQA GCSE Maths

Multiplying Decimals — GCSE RevisionWatch the walkthrough, then read the notes below.

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What you'll learn

Add and subtract decimals
Multiply and divide decimals
Convert between fractions and decimals
Recognise terminating and recurring decimals

Calculating with decimals

To add or subtract, line up the decimal points. To multiply, ignore the points, multiply as whole numbers, then put back the total number of decimal places. To divide by a decimal, make the divider a whole number first by multiplying both numbers by 10, 100, …

1Ignore points:

3 \times 2 = 6

2There are 2 decimal places in total, so the answer has 2 d.p.

0.3 \times 0.2 = 0.06

Answer

0.06

Tip — Count the decimal places in the question — the answer to a multiplication has the same total.

Fractions and decimals

A fraction becomes a decimal by dividing the top by the bottom. A fraction gives a $terminating$ decimal if its denominator only has factors of 2 and 5; otherwise it $recurs$ (e.g. $\frac{1}{3} = 0.333 \dots = 0. \dot{3}$ ).

Remember these

\frac{1}{4} = 0.25

Divide top by bottom to convert.

0. \dot{3} = \frac{1}{3}

Recurring decimal.

Watch out for these

Writing

0.3 \times 0.2 = 0.6

Count decimal places: the answer is

0.06

Not lining up the decimal points when adding.

Keep points in a vertical line, filling gaps with zeros.

Key takeaways

Line up points to add/subtract.
For ×, multiply as whole numbers then replace the decimal places.
Divide top by bottom to turn a fraction into a decimal.

Test yourself

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