GCSE Maths Practice: decimals

Question 5 of 10

A multi-step Higher GCSE decimals task involving multiplication, subtraction, and division before rounding to 3 significant figures. Precision and estimation are crucial.

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\( \begin{array}{l} \textbf{Calculate } ((1.35\times1.12)-0.318) \div 0.652,\\ \textbf{giving your answer to 3 s.f.} \end{array} \)

Choose one option:

Estimate each stage first to spot decimal-point mistakes. Always round once, at the end, to 3 significant figures.

This Higher-tier decimals problem involves three operations in sequence (multiplication, subtraction, and division) followed by rounding to a specified degree of accuracy. All intermediate values must be kept exact to avoid losing precision before the final rounding stage.

Full Working

  1. Multiply: \(1.35\times1.12=1.512\). Ignore decimals first (135×112=15120), then place four decimal places.
  2. Subtract: \(1.512-0.318=1.194\). Line up decimal places to avoid misalignment errors.
  3. Divide: \(1.194\div0.652\approx1.832515\ldots\). Because the divisor is below 1, the result should be larger than 1.194 — a useful magnitude check.
  4. Round to 3 significant figures: 1.8325… becomes 1.83 because the 4th significant figure (2) does not round the 3rd up.

Estimation Check

1.35≈1.4 and 1.12≈1.1 → 1.4×1.1≈1.54. Subtract about 0.3 gives ≈1.24. Dividing by 0.65 roughly doubles the value → ≈1.9. The final exact result 1.83 is close to this estimate, supporting correct decimal placement.

Common Errors

  • Rounding 1.512 early to 1.51 or 1.5, causing a different final 3 s.f. answer.
  • Dividing by 0.652 as if dividing by 652 or 6.52 (decimal drift).
  • Confusing 3 significant figures with 3 decimal places.

Extension

Try altering the final division to \(\div0.598\) or rounding to 2 s.f. instead. This strengthens fluency with rounding rules and decimal magnitude.