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 fully worked examples at both tiers, flags the errors examiners see year after year, and finishes with practice questions you can try right now. For a wider view of what to cover, check our complete GCSE Maths topics list.

What Is a Decimal?

A decimal is a way of writing numbers that are not whole, using a decimal point to separate the whole-number part from the fractional part. Each digit after the decimal point represents a fraction of a power of ten.

So the number 3.47 means 3 ones, 4 tenths, and 7 hundredths.

Key Relationships

Ordering Decimals

To order decimals, compare digits column by column from left to right. If needed, pad shorter decimals with trailing zeros so every number has the same number of decimal places. For example, to compare 0.6 and 0.59: rewrite 0.6 as 0.60, then compare — 60 hundredths is greater than 59 hundredths, so 0.6 > 0.59.

Step-by-Step Method

Adding and Subtracting Decimals

1. Write the numbers in a column, lining up the decimal points directly above one another.
2. Pad with zeros if the numbers have different numbers of decimal places.
3. Add or subtract as you would with whole numbers, starting from the rightmost column.
4. Bring the decimal point straight down into your answer.

Multiplying Decimals

1. Ignore the decimal points and multiply the numbers as if they were whole numbers.
2. Count the total number of decimal places in both original numbers.
3. Place the decimal point in your answer so it has that total number of decimal places.

For example, 0.3 × 0.12: multiply 3 × 12 = 36. There are 1 + 2 = 3 decimal places in total, so the answer is 0.036.

Dividing Decimals

1. If the divisor (the number you are dividing by) is a decimal, multiply both the divisor and the dividend by 10, 100, or 1000 until the divisor becomes a whole number.
2. Carry out the division using short or long division.
3. Keep the decimal point in place in your answer.

Rounding Decimals

1. Identify the digit in the place you are rounding to.
2. Look at the next digit to the right.
3. If it is 5 or more, round up. If it is less than 5, round down (keep the digit the same).
4. Remove all digits after the rounding position.

Worked Example 1 — Foundation Level

Question: Calculate 4.6 + 3.85, then round your answer to one decimal place.

Working:

Step 1 — Line up the decimal points and pad:

  4.60
+ 3.85
------
  8.45

Step 2 — Round 8.45 to one decimal place. The digit in the tenths column is 4. The next digit is 5, so round up.

Answer: 8.5

Worked Example 2 — Higher Level

Question: Without a calculator, work out 0.24 × 0.035.

Working:

Step 1 — Multiply as whole numbers: 24 × 35. 24 × 35 = 24 × 30 + 24 × 5 = 720 + 120 = 840

Step 2 — Count decimal places: 0.24 has 2 decimal places; 0.035 has 3 decimal places. Total = 5.

Step 3 — Place the decimal point: 840 with 5 decimal places = 0.00840 = 0.0084.

Answer: 0.0084

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.

Practice Questions

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.

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Related Topics

• Fractions
• Percentages
• Standard Form
• Bounds and Error Intervals

Summary

• Decimals use place value columns (tenths, hundredths, thousandths) after the decimal point.
• Line up decimal points when adding or subtracting.
• When multiplying decimals, count total decimal places and apply to the product.
• When dividing by a decimal, multiply both numbers to make the divisor whole.
• Round by checking the digit to the right of your rounding position.
• Learn common fraction-to-decimal conversions to save time in exams.
• Always estimate to check whether your answer is reasonable.