GCSE Maths Practice: decimals

Question 5 of 10

This Higher GCSE problem tests dividing one decimal by another — a vital skill for ratio, percentage, and rate calculations. Precision and estimation help ensure your decimal placement is correct.

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\( \begin{array}{l} \textbf{Calculate } 0.84 \div 0.3.\end{array} \)

Choose one option:

Estimate first: 0.84 is close to 0.9 and 0.3 is close to 1/3, so the result should be around 3. Your exact answer 2.8 is close — decimal point confirmed.

Dividing by decimals becomes easier when you eliminate the decimals by multiplying both numbers by a power of ten. This technique simplifies calculations without changing the value of the expression.

Worked Examples

  1. Example 1: Divide 0.96 ÷ 0.4.
    Write as \(\frac{0.96}{0.4}\). Multiply both by 10 → \(\frac{9.6}{4}\). Then divide: 9.6 ÷ 4 = 2.4.
  2. Example 2: Divide 1.68 ÷ 0.6.
    Multiply both by 10 → \(\frac{16.8}{6}\). 16.8 ÷ 6 = 2.8.
  3. Example 3: Divide 7.5 ÷ 0.25.
    Multiply both by 100 → \(\frac{750}{25}\). 750 ÷ 25 = 30.

Reasoning & Estimation

Before dividing, estimate: 0.84 ÷ 0.3 is roughly (0.9 ÷ 0.3) = 3, so the answer should be slightly below 3. This confirms that 2.8 is a realistic result.

Common Mistakes

  • Forgetting to multiply both numbers by the same power of ten.
  • Misplacing the decimal after division — always check with estimation.
  • Confusing 0.3 (three tenths) with 3 — dividing by 0.3 actually multiplies the value by about 3⅓.

Extra Challenge

Try a variant: 0.84 ÷ 0.07. Multiply both by 100 → \(\frac{84}{7}\). Answer: 12. Notice how a smaller divisor makes the quotient much larger.

Exam Tip

After dividing, always check by reversing: multiply the answer by the divisor — if you get back to the original number, your result is correct.