Decimals

Decimals are numbers with a fractional part shown after a decimal point. You need to add, subtract, multiply and divide decimals, and round to a given number of decimal places or significant figures.

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Key facts to remember

1To add or subtract decimals: line up the decimal points.
2To multiply decimals: ignore the decimal point, multiply as integers, then place the decimal point back.
3To divide by a decimal: multiply both numbers by 10 (or 100 etc.) to make the divisor an integer.
4Rounding to d.p.: look at the (d+1)th digit — if 5 or more, round up; if less than 5, round down.
5Rounding to significant figures: the first significant figure is the first non-zero digit.
61 decimal place = nearest tenth; 2 d.p. = nearest hundredth.

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Worked examples

Example 1

Work out 3.6 × 0.04

Working

Ignore decimal points: 36 × 4 = 144
3.6 has 1 decimal place, 0.04 has 2 decimal places → 3 decimal places total
Place decimal point 3 places from the right: 0.144

Answer0.144

Example 2

Work out 5.76 ÷ 0.8

Working

Multiply both by 10 to eliminate the decimal in the divisor: 57.6 ÷ 8
57.6 ÷ 8 = 7.2

Answer7.2

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Common mistakes

✗Not lining up decimal points when adding or subtracting, leading to place value errors.

✗Forgetting to count the total decimal places when multiplying.

✗Rounding 6.45 to 1 d.p. as 6.4 instead of 6.5 — the digit after is 5, so round up.

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Exam tips

✓When multiplying decimals, count total decimal places in both numbers — your answer must have that many.

✓For division by a decimal, write it as a fraction and multiply top and bottom to clear the decimal.

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