GCSE Maths Practice: decimals

Question 4 of 10

A multi-step decimals task: multiply, subtract, then divide, finally giving the result to 3 significant figures.

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\( \begin{array}{l} \textbf{Calculate } ((1.75\times0.48)-0.035)\div0.5,\\ \textbf{giving your answer to 3 significant figures.} \end{array} \)

Choose one option:

Estimate each stage (≈0.875→0.84→÷0.5≈1.68) to check magnitude, then compute exactly and round once.

This Higher-tier decimals problem chains multiplication, subtraction, and division, then applies rounding to a stated accuracy. Keeping full precision until the final step prevents accumulated rounding error.

Method Outline

  1. Multiply: 1.75 × 0.48 = 0.84. (Ignore decimals first: 175×48=8400, then place four decimal places → 0.8400.)
  2. Subtract: 0.84 − 0.035 = 0.805. Align decimal places carefully; write 0.840 − 0.035 if needed.
  3. Divide: 0.805 ÷ 0.5 = 1.61. Note that dividing by 0.5 is multiplying by 2, so the value should double.
  4. Rounding: 1.61 is already at 3 significant figures.

Estimation & Reasonableness

1.75×0.5≈0.875; subtract ≈0.035 → ≈0.84; divide by 0.5 doubles → ≈1.68. The exact result 1.61 is close, confirming correct magnitude and decimal placement.

Common Pitfalls

  • Rounding 0.84 early to 0.8, which shifts the final figure.
  • Misreading ÷0.5 as halving; it actually doubles.
  • Misaligning decimals in 0.84 − 0.035.

Technique Tip

Annotate each intermediate result and keep all digits until the final rounding instruction. This preserves accuracy and earns method marks in exams.