GCSE Maths Practice: decimals

Question 9 of 10

A multi-step decimals task: convert a decimal to a simplified fraction, then express it as a percentage. Precision in the simplification step is essential.

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\( \begin{array}{l} \textbf{Convert } 0.475 \textbf{ to a fraction in simplest form,}\\ \textbf{then write it as a percentage.} \end{array} \)

Choose one option:

Estimate: 0.475 is close to 0.5 → about 50%. Expect a result slightly below 50%, which matches 47.5%.

Higher-tier focus: This task links three representations of the same value: decimal → fraction → percentage. You must simplify exactly before converting to a percentage to avoid rounding drift.

Method Recap

  1. Decimal → Fraction: count decimal places and put the number over the matching power of ten; then simplify using the HCF.
  2. Fraction → Percentage: multiply by 100% (or create a denom­inator of 100 and read off the percent).

Worked Examples

A. Convert 0.375 → fraction → percentage.
0.375 = 375/1000 = 3/8; 3/8 × 100% = 37.5%.

B. Convert 0.84 → fraction → percentage.
0.84 = 84/100 = 21/25; 21/25 × 100% = 84%.

C. Convert 0.125 → fraction → percentage.
0.125 = 125/1000 = 1/8; 1/8 × 100% = 12.5%.

Common Pitfalls

  • Not simplifying 475/1000 fully (must reach 19/40).
  • Forgetting to attach the % symbol after multiplying by 100.
  • Mixing up decimal places with percentage (47.5 is not 47.5%).

Quick Check

Since 0.475 is just under 0.5, the percent should be just under 50% → 47.5% is reasonable.