GCSE Maths Practice: decimals

Question 10 of 10

This foundation-level GCSE Maths question tests your understanding of how to compare decimals and fractions. It helps you develop number sense by recognising which values are larger or smaller and how to compare them effectively.

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\( \begin{array}{l}\textbf{Which is greater: } 0.9 \textbf{ or } \frac{4}{5}\textbf{?}\end{array} \)

Choose one option:

To compare decimals and fractions, convert both to the same form. Either write both as decimals or both as fractions. Then compare their numerical values directly.

Comparing Decimals and Fractions

Fractions and decimals describe the same idea — parts of a whole — but are written in different ways. To decide which is larger, it often helps to write both in the same form. In this example, we have 0.9 (a decimal) and \(\frac{4}{5}\) (a fraction). Converting one of them makes comparison easier.

If we change \(\frac{4}{5}\) to a decimal, we divide 4 by 5 to get 0.8. Now it’s clear that 0.9 is greater because 0.9 is closer to 1 than 0.8 is. This technique works for any pair of decimals and fractions.

Step-by-Step Method

  1. Identify which number is a fraction and which is a decimal.
  2. Choose to convert either the fraction into a decimal or the decimal into a fraction — whichever seems simpler.
  3. Compare the results. The number with the greater value is larger.

Worked Examples

Example 1: Compare 0.6 and \(\frac{3}{5}\).
\(\frac{3}{5} = 0.6\), so they are equal.

Example 2: Compare 0.75 and \(\frac{2}{3}\).
\(\frac{2}{3} = 0.666...\), so 0.75 is greater.

Example 3: Compare 0.4 and \(\frac{1}{2}\).
\(\frac{1}{2} = 0.5\), so 0.4 is smaller.

Example 4: Compare 0.2 and \(\frac{1}{5}\).
\(\frac{1}{5} = 0.2\), so they are equal.

Common Mistakes

  • Not converting: Comparing 0.9 and \(\frac{4}{5}\) directly without conversion can be misleading. Always express both in the same form first.
  • Rounding too soon: When converting repeating decimals, don’t round too early — compare after a few decimal places for accuracy.
  • Mixing up greater/less than symbols: Remember that the number further to the right on a number line is always larger.

Real-Life Applications

Comparing decimals and fractions is a common skill in everyday life. For example, deciding between discounts — one store offers 0.8 off (80%) and another offers \(\frac{3}{4}\) off (75%) — requires you to know that 0.8 is greater. In measurements, you might compare 0.9 metres and \(\frac{4}{5}\) of a metre to decide which is longer. In probability, 0.9 means a 90% chance, while \(\frac{4}{5}\) means 80% — the higher probability wins.

FAQs

1. Which is easier to compare — decimals or fractions?
Decimals are often easier because you can line them up and compare digits place by place.

2. What if both are fractions?
Find a common denominator and compare numerators.

3. What if both are decimals?
Align them by the decimal point and compare from left to right.

4. Why learn both forms?
Because exams, calculators, and real-world data use both — flexibility helps you adapt to any context.

Study Tip

When practising, switch between fraction-to-decimal and decimal-to-fraction comparison. Write quick notes such as \(\frac{1}{2}=0.5\), \(\frac{3}{4}=0.75\), \(\frac{4}{5}=0.8\), \(\frac{9}{10}=0.9\). These are benchmark equivalents that make future comparisons nearly instant.

Being able to compare fractions and decimals is key to number fluency in GCSE Maths — it strengthens your estimation, reasoning, and confidence with everyday quantities.