GCSE Maths Practice: decimals

Question 4 of 10

A multi-step Higher GCSE decimals task: subtract, then multiply, and finally round the result to 3 significant figures. Accuracy and estimation both matter.

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\( \begin{array}{l} \textbf{Calculate } (3.25-0.625)\times0.75,\\ \textbf{giving your answer to 3 s.f.} \end{array} \)

Choose one option:

Estimate first: (3.25−0.6)≈2.65 and 2.65×0.75≈2.0. A final answer slightly below 2.0 is expected; 1.97 fits.

Higher-tier focus: This problem chains decimal subtraction and multiplication, then requires rounding to a stated accuracy (3 significant figures). The key is to keep full precision during working and round once at the end.

Concept overview

Subtraction with decimals: align decimal points; if needed, pad with trailing zeros (e.g., 3.250 − 0.625).
Multiplying by a decimal: multiply as integers, then place the decimal using the total number of decimal places in the factors.
Rounding to significant figures (s.f.): count from the first non-zero digit. Look at the next digit to decide whether to round up or keep.

Worked Example A (same structure)

Compute \((4.8 - 1.375) \times 0.62\) to 3 s.f.

  1. 4.800 − 1.375 = 3.425.
  2. 3.425 × 0.62 = 2.122 + 0.061 = 2.1235 (or calculator).
  3. 3 s.f.: 2.1235 → 2.12.

Worked Example B (decimal places differ)

Compute \((2.035 - 0.48) \times 0.7\) to 3 s.f.

  1. 2.035 − 0.480 = 1.555.
  2. 1.555 × 0.7 = 1.0885.
  3. 3 s.f.: 1.0885 → 1.09.

Worked Example C (estimation check)

Estimate \((3.25 - 0.625) \times 0.75\).

  1. 3.25 − 0.625 ≈ 3.25 − 0.6 = 2.65.
  2. 2.65 × 0.75 ≈ (2.65 × 3)/4 = 7.95/4 ≈ 1.99.
  3. Exact answer 1.96875 ≈ 1.97 (3 s.f.), close to the estimate.

Error-spotting mini checklist

  • Premature rounding? Keep 1.96875 intact until the end.
  • Wrong s.f./d.p.? 3 s.f. for 1.96875 is 1.97; 3 d.p. would be 1.969 — different rule.
  • Misaligned subtraction? Always write 3.250 − 0.625.
  • Decimal placement in product? If you get 19.6875 or 0.196875, you misplaced the decimal.

Why multiplying by 0.75 reduces the value

Since 0.75 < 1, the product must be smaller than 2.625. Also, 0.75 = 3/4, so \(2.625 \times 0.75 = (2.625 \times 3)/4\), i.e., “three quarters of 2.625”. This magnitude check helps catch keypad errors.

Practice variants

  1. \((3.25 - 0.625) \times 0.74\) to 3 s.f. → 1.94.
  2. \((3.250 - 0.620) \times 0.75\) to 3 s.f. → 1.97.
  3. \((3.25 - 0.625) \times 0.75\) to 2 d.p. → 1.97.

Exam tip: Box each intermediate value and annotate it with the operation (−, ×). Finish with a single rounding step to the requested accuracy.