GCSE Maths Practice: decimals

Question 3 of 10

This GCSE Maths foundation question helps you practise dividing decimals by powers of ten — 10, 100, or 1000. It develops understanding of place value and prepares you for unit conversions and ratio scaling questions.

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\( \begin{array}{l}\textbf{Calculate } 4.2 \div 10.\end{array} \)

Choose one option:

When dividing by powers of ten, move the digits to the right or the decimal point to the left. The number becomes smaller by one place value for each zero in the divisor.

Understanding Division by Powers of Ten

Decimals behave predictably when divided by 10, 100, or 1000. Each division moves every digit one place to the right on the place value chart. This makes the number ten, one hundred, or one thousand times smaller. Mastering this pattern is vital in GCSE Maths for calculations involving money, measurements, and ratios.

Step-by-Step Method

  1. Count the number of zeros in the divisor (e.g. 10 → one zero, 100 → two, 1000 → three).
  2. Move the decimal point that many places to the left.
  3. Fill any empty spaces with zeros if necessary.
  4. Check that your answer is smaller than the starting number — division should always reduce the value.

Worked Examples

Example 1: 5.6 ÷ 10 = 0.56
Move one place left → 0.56.

Example 2: 3.7 ÷ 100 = 0.037
Move two places left → 0.037.

Example 3: 42 ÷ 1000 = 0.042
Move three places left → 0.042.

Example 4: 0.8 ÷ 10 = 0.08
Move one place left → 0.08.

Notice that every time you divide by ten, the decimal moves left, shrinking the number proportionally.

Common Mistakes

  • Moving the decimal the wrong way: Dividing always moves it left, multiplying moves it right.
  • Dropping zeros: Always keep necessary placeholder zeros to maintain correct place value.
  • Forgetting that division makes numbers smaller: If your answer gets bigger, you’ve moved the decimal the wrong way.

Real-Life Applications

Understanding how to divide decimals by powers of ten helps with unit conversions and scaling. For example, converting centimetres to metres (divide by 100), or millilitres to litres (divide by 1000). If a bottle holds 4.2 litres, that’s 4200 millilitres — dividing by 1000 gives 4.2 litres again. Similarly, dividing £4.20 by 10 represents one tenth of the cost, or £0.42. These quick mental operations save time in exams and everyday problem solving.

FAQs

1. Why move the decimal left when dividing?
Because each division by 10 makes the number ten times smaller — shifting place values to the right on the chart.

2. Does the same rule work for all decimals?
Yes, whether it’s 3.5 or 0.007, you move the decimal one, two, or three places depending on how many zeros there are in the divisor.

3. What happens if there aren’t enough digits?
Add zeros to the left of the number as placeholders (e.g. 3 ÷ 100 = 0.03).

4. What’s the reverse of dividing by 10?
Multiplying by 10 — which moves the decimal the same number of places to the right.

Study Tip

Write a simple place value chart: thousands, hundreds, tens, ones, tenths, hundredths, thousandths. Then slide a number like 4.2 left or right to visualise the movement. Practising with both multiplication and division will make your understanding of powers of ten automatic.

Being fluent at dividing by powers of ten builds solid number sense, making topics like unit conversion, scaling, and ratio much easier throughout GCSE Maths.