GCSE Maths Practice: decimals

Question 6 of 10

This question develops your understanding of converting decimals into fractions and simplifying to their lowest terms. Precision in simplification is vital at higher GCSE level.

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\( \begin{array}{l}\textbf{Convert } 0.45 \textbf{ to a fraction in its simplest form.}\end{array} \)

Choose one option:

Recognise common percentage links — 45% equals 0.45, which simplifies to \(\frac{9}{20}\). Linking decimals, fractions, and percentages strengthens numerical fluency.

Decimals with two digits after the point represent hundredths. Converting them to fractions helps strengthen understanding of place value and simplifying ratios.

Worked Examples

Example 1: Convert 0.35 to a fraction.

  1. \(0.35 = \frac{35}{100}\)
  2. Simplify: \(\frac{35}{100} = \frac{7}{20}\)

Example 2: Convert 0.6 to a fraction.

  1. \(0.6 = \frac{6}{10}\)
  2. Simplify: \(\frac{6}{10} = \frac{3}{5}\)

Example 3: Convert 0.125 to a fraction.

  1. \(0.125 = \frac{125}{1000}\)
  2. Simplify: \(\frac{125}{1000} = \frac{1}{8}\)

Tip: Numbers ending in 5 or 0 are divisible by 5 — a useful shortcut for simplifying hundredths-based fractions.

This process supports working with percentages (e.g., 45% = \(\frac{9}{20}\)) and ratio simplifications in algebraic and statistical contexts.