GCSE Maths Practice: decimals

Question 7 of 10

A challenging multi-step decimals question: combine addition, multiplication, subtraction and division, then round to 3 significant figures with care.

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\( \begin{array}{l}\text{Calculate ((0.987+0.654)}\times0.75-0.123)\div\;0.456,\\\text{giving your answer to 3 s.f.} \end{array} \)

Choose one option:

Estimate at each stage to sanity-check size, then compute exactly and round once to 3 significant figures.

This Higher-tier decimals problem chains four skills: addition, multiplication, subtraction, and division, followed by rounding to significant figures. Accuracy depends on keeping full precision until the very end and applying the rounding rule only once.

Method Outline

  1. Add: 0.987 + 0.654 = 1.641. Align decimal points and work column by column to avoid place-value slips.
  2. Multiply: 1.641 × 0.75 = 1.23075. Since 0.75 = 3/4, this step should reduce the value to roughly three quarters of 1.641, which is consistent with 1.23…
  3. Subtract: 1.23075 − 0.123 = 1.10775. Keep all digits; rounding early can change the third significant figure later.
  4. Divide: 1.10775 ÷ 0.456 ≈ 2.429276… Because the divisor is less than 1, the result should be larger than 1.10775 — a useful magnitude check.
  5. Round to 3 s.f.: 2.429… → 2.43 (the fourth significant digit is 9, so the third rounds up).

Reasonableness via Estimation

Quick estimate: (1.0 + 0.65) ≈ 1.65; × 0.75 ≈ 1.24; − 0.12 ≈ 1.12; then ÷ 0.46 ≈ 2.43. The estimate closely matches the exact result, confirming correct decimal placement.

Common Mistakes

  • Premature rounding: Rounding 1.23075 to 1.23 before subtraction can shift the final 3 s.f.
  • Decimal drift in division: Mis-keying 0.456 as 0.465 or 0.45 changes the quotient’s scale. Re-enter carefully.
  • Confusing s.f. with d.p.: Three significant figures for 2.429… is 2.43, not 2.429 (that would be 3 decimal places).

Technique Tips

Write intermediate results on separate lines and annotate with the operation ( +, ×, −, ÷ ). This keeps place value clear and makes it easy to backtrack if your final magnitude looks off.

Extension

Try changing the divisor to 0.48 or the multiplier to 0.74 and compare the sensitivity of the final rounded value. This builds intuition about how small changes propagate through a chain of decimal operations.