Decimals
This free Foundation and Higher GCSE Maths worksheet on 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 adding or subtracting decimals, line up the decimal points.
Free downloads
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.
Topic overview
Decimals extend place value beyond the units column into tenths, hundredths and thousandths. Each column is one tenth of the one to its left, continuing the same pattern as whole numbers.
That structure is what makes decimal arithmetic work. Adding and subtracting require the decimal points to be aligned so that tenths meet tenths. Multiplying and dividing by powers of ten shift the digits rather than changing them.
Decimals appear constantly in money, measurement and percentages, so fluency here pays off across the whole paper. The most valuable habit is padding with trailing zeros: writing \(0.4\) as \(0.40\) costs nothing and prevents most comparison and alignment errors.
Revision notes
Decimal place value
After the point, the columns are tenths, hundredths and thousandths. In \(3.472\), the \(4\) is four tenths, the \(7\) is seven hundredths and the \(2\) is two thousandths.
A trailing zero does not change the value, so \(0.5 = 0.50 = 0.500\). Adding them makes numbers easier to compare and to line up.
Multiplying and dividing by powers of ten
Multiplying by \(10\) shifts every digit one column left; dividing shifts them right.
So \(0.36 \times 100 = 36\) and \(4.2 \div 100 = 0.042\). Think of the digits moving rather than the point, since the point stays fixed between units and tenths.
Terminating and recurring decimals
A fraction gives a terminating decimal when its denominator has only \(2\) and \(5\) as prime factors, such as \(\frac{3}{8} = 0.375\).
Otherwise the decimal recurs, so \(\frac{1}{3} = 0.333\ldots\), written \(0.\dot{3}\). A dot marks the repeating digit, or dots mark the first and last of a repeating block.
Key points
- Columns after the point are tenths, hundredths, thousandths.
- Trailing zeros do not change a decimal's value.
- Multiplying by 10 moves digits one place left.
- Dividing by 10 moves digits one place right.
- Line up decimal points when adding or subtracting.
- A denominator with only 2s and 5s gives a terminating decimal.
Worked examples
Example 1
Work out \(0.47 \times 1000\).
Working
Example 2
Put \(0.7\), \(0.68\) and \(0.705\) in ascending order.
Working
Example 3
Write \(\frac{7}{8}\) as a decimal.
Working
Common mistakes
Assuming a longer decimal is larger.
0.68 has more digits than 0.7 but is smaller. Pad with zeros and compare column by column.
Moving the decimal point instead of the digits.
The point stays fixed between units and tenths. It is the digits that shift.
Dropping a zero when multiplying.
0.47 × 1000 is 470, not 47. The zero holds the units column.
Writing a recurring decimal without the dot.
0.333 is not the same as 0.3 recurring. The dot notation is required.
Exam tips
- Pad decimals with trailing zeros before comparing or adding.
- Check the size of your answer after multiplying by a power of ten.
- Use dot notation for recurring decimals.
- Convert fractions to decimals by dividing the top by the bottom.
Key terms
- Tenth
- The first column after the decimal point.
- Terminating decimal
- A decimal that stops after a finite number of digits.
- Recurring decimal
- A decimal with a digit or block that repeats forever.
- Trailing zero
- A zero at the end of a decimal that does not change its value.
Related topics
Written and reviewed against the current AQA, Edexcel and OCR specifications. Spotted an error? Let us know.