GCSE Maths Practice: decimals

Question 6 of 10

This GCSE Maths foundation question helps you practise converting decimals into fractions. Understanding this process builds confidence when working with percentages, ratios, and measurements.

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\( \begin{array}{l}\textbf{Convert } 0.05 \textbf{ to a fraction in its simplest form.}\end{array} \)

Choose one option:

Look carefully at the place value of the final digit. Two decimal places mean hundredths, three mean thousandths. Always simplify your fraction to lowest terms.

Understanding Decimals and Fractions

Decimals and fractions are two different ways to represent the same idea — parts of a whole. Every decimal can be written as a fraction, and every fraction can be written as a decimal. In GCSE Maths, you must be able to move confidently between the two forms.

When you see a decimal such as 0.05, the digit 5 is in the hundredths place because it is two digits to the right of the decimal point. This means that 0.05 equals five hundredths, or \(\frac{5}{100}\).

Step-by-Step Conversion

  1. Write the decimal as a fraction using its place value. For two decimal places, use 100 as the denominator.
  2. Simplify the fraction by dividing both numerator and denominator by their highest common factor (HCF).
  3. Check whether the fraction can be reduced further.

For example:

  1. 0.05 = \(\frac{5}{100}\)
  2. Divide both by 5 → \(\frac{1}{20}\)
  3. Final answer: \(\frac{1}{20}\)

Worked Examples

Example 1: Convert 0.2 to a fraction.
0.2 = \(\frac{2}{10}\) → simplify by 2 → \(\frac{1}{5}\).

Example 2: Convert 0.35 to a fraction.
0.35 = \(\frac{35}{100}\) → divide by 5 → \(\frac{7}{20}\).

Example 3: Convert 0.125 to a fraction.
0.125 = \(\frac{125}{1000}\) → divide by 125 → \(\frac{1}{8}\).

Common Mistakes

  • Using the wrong denominator (for example, writing 0.05 as \(\frac{5}{10}\)). Remember that the number of digits after the decimal determines the power of ten in the denominator.
  • Forgetting to simplify the fraction fully.
  • Mixing up tenths and hundredths — always count decimal places.

Real-Life Connections

Decimal-to-fraction conversions appear everywhere in daily life. In finance, £0.05 means five pence out of £1, or one-twentieth. In measurement, 0.05 m equals one-twentieth of a metre (5 cm). Understanding these relationships makes it easier to estimate, compare quantities, and check your calculations in practical tasks.

FAQs

1. Why do decimals and fractions represent the same value?
Because both show division — a decimal is another way of writing a numerator divided by a power of ten.

2. How do I know what denominator to use?
Count decimal places: one → tenths (10), two → hundredths (100), three → thousandths (1000).

3. What if the decimal repeats?
Repeating decimals can still be converted to fractions, but you must use algebraic methods (these appear in higher-level GCSE topics).

Study Tip

To strengthen your understanding, practise reading decimals aloud with their place values — for example, 0.05 as “five hundredths.” This habit helps avoid confusion in exams.

Converting decimals to fractions is a fundamental GCSE Maths skill that connects place value, division, and simplification. Master it early — it will help with percentages, ratios, and algebraic fractions later on.