Sheet № 02 · Foundation + Higher · AQA · Edexcel · OCR
Decimals –
Decimals are everywhere — from price tags and measurements to exam questions worth several marks. Every GCSE Maths student on Foundation and Higher tier needs to add, subtract, multiply, and divide decimals confidently, as well as convert between decimals, fractions, and percentages. This guide explains each skill step by step, gives you
§Key definitions
Question:
Calculate 4.6 + 3.85, then round your answer to one decimal place.
Q1 (Foundation):
Work out 12.3 − 4.78.
Q2 (Foundation):
Arrange these decimals in ascending order: 0.305, 0.35, 0.3, 0.053.
Q3 (Higher):
Calculate 7.2 ÷ 0.016 without a calculator.
§Formulas to memorise
To convert a fraction to a decimal, divide the numerator by the denominator: a/b = a ÷ b
To convert a decimal to a percentage, multiply by 100: 0.35 = 35%
A recurring decimal can be written using dot notation: 1/3 = 0.333... = 0.3̇
Worked example
Calculate 4.6 + 3.85, then round your answer to one decimal place.
Working:
⚠ Common mistakes
- ✗Misaligning the decimal points when adding or subtracting. Always line up the points vertically. Misalignment leads to digits being added in the wrong columns.
- ✗Placing the decimal point incorrectly after multiplying. Count the decimal places in both original numbers carefully and apply the total to your product.
- ✗Forgetting to adjust both numbers when dividing by a decimal. If you multiply the divisor by 10, you must also multiply the dividend by 10 to keep the calculation equivalent.
- ✗Confusing rounding with truncating. Rounding follows the "5 or more, round up" rule. Truncating simply removes digits without rounding. The question will specify which to use.
- ✗Writing unnecessary trailing zeros as part of a rounded answer. If a question says "round to 1 decimal place", writing 8.50 is technically correct but 8.5 is the cleaner convention. Follow the exam board's mark scheme style.
✦ Exam tips
- →On non-calculator papers, set out column addition and multiplication neatly. Examiners award method marks for clear, correct working even if you make a small arithmetic slip.
- →Use estimation to check your answer. For example, 3.9 × 5.1 is roughly 4 × 5 = 20. If your answer is nowhere near 20, recheck your working. Our revision strategies guide has more tips on checking answers efficiently.
- →Know the common fraction-to-decimal conversions by heart: 1/2 = 0.5, 1/4 = 0.25, 1/5 = 0.2, 1/8 = 0.125, 1/3 = 0.333..., and so on. These save time across many questions.
- →Watch for questions that combine decimals with other topics like area, perimeter, or probability — the decimal skills are the same, but the context changes.
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