GCSE Maths Practice: decimals

Question 5 of 10

This foundation GCSE Maths question practises dividing a whole number by a decimal. It strengthens understanding of how multiplying and dividing by powers of ten affect place value.

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\( \begin{array}{l}\textbf{Calculate } 6 \div 0.3.\end{array} \)

Choose one option:

To divide by a decimal, multiply both numbers by the same power of ten to make the divisor a whole number. This keeps the calculation equivalent but easier to perform.

Dividing by a Decimal

Dividing by decimals can seem tricky at first, but the rule is simple: make the divisor a whole number by multiplying both numbers by the same power of ten. This uses place value to shift the decimal point rather than changing the size of the number.

Step-by-Step Method

  1. Write the division as a fraction: 6 ÷ 0.3 = 6 / 0.3.
  2. Multiply both numerator and denominator by 10 to remove the decimal in the denominator: (6 × 10) / (0.3 × 10) = 60 / 3.
  3. Perform the division: 60 ÷ 3 = 20.
  4. Check that the result makes sense — dividing by less than 1 should make the answer larger.

Worked Examples

Example 1: 4 ÷ 0.2
4 / 0.2 = (4 × 10) / (0.2 × 10) = 40 / 2 = 20.

Example 2: 8 ÷ 0.4
8 / 0.4 = (8 × 10) / (0.4 × 10) = 80 / 4 = 20.

Example 3: 12 ÷ 0.5
12 / 0.5 = (12 × 10) / (0.5 × 10) = 120 / 5 = 24.

Example 4: 9 ÷ 0.3
9 / 0.3 = (9 × 10) / (0.3 × 10) = 90 / 3 = 30.

Common Mistakes

  • Forgetting to adjust both numbers: You must multiply both the dividend and divisor by the same power of ten.
  • Assuming the answer will be smaller: When dividing by a number less than 1, the answer actually gets larger.
  • Incorrect decimal movement: Count how many places to move the decimal point — one place for tenths, two for hundredths, and so on.

Real-Life Applications

Dividing by decimals appears frequently in practical problems, such as:
• Working out unit prices: £6 ÷ 0.3 kg = £20 per kg.
• Calculating rates: 6 litres ÷ 0.3 hours = 20 litres per hour.
• Measuring efficiency or concentration in science.

This method also helps when finding percentages, scaling recipes, or adjusting ratios.

FAQs

1. Why multiply by 10?
Because multiplying by 10 moves the decimal one place to the right, making the divisor a whole number while keeping the division equivalent.

2. What if the divisor has two decimal places?
Then multiply both numbers by 100 to remove both decimals.

3. How can I check my answer?
Multiply your result by the divisor — 20 × 0.3 = 6, so it’s correct.

4. Does this work for any decimals?
Yes, it works for any positive decimal, and the same logic extends to dividing by 0.03 or 0.007.

Study Tip

Practise with examples where the decimal moves one, two, or three places. Start with 4 ÷ 0.2, then 4 ÷ 0.02, and 4 ÷ 0.002 to see how the answer changes. Recognising this pattern helps you spot place-value relationships quickly during exams.

Understanding how to divide by decimals builds confidence for higher-level arithmetic, ratio, and percentage problems in GCSE Maths.