GCSE Maths Practice: decimals

Question 1 of 10

This foundation GCSE Maths question helps you practise comparing decimals. Recognising which number is larger by analysing place values is a key skill in number reasoning and estimation.

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\( \begin{array}{l}\textbf{Which number is largest? } 0.45,\; 0.5,\; 0.48.\end{array} \)

Choose one option:

Always line decimals up by their decimal points and compare digits from left to right — tenths first, then hundredths, and so on. Add zeros if needed to make each number the same length (e.g. 0.5 = 0.50).

Comparing and Ordering Decimals

When comparing decimals, think of place value as you would with whole numbers. The closer a digit is to the decimal point, the more significant its value. Start by comparing tenths, then move to hundredths, thousandths, and so on.

Step-by-Step Method

  1. Write the numbers vertically, aligning the decimal points.
  2. Fill in zeros to make them the same length if necessary (e.g. 0.5 = 0.50).
  3. Compare digits from left to right — start with tenths, then hundredths.
  4. The number with the larger first differing digit is greater.

Worked Examples

Example 1: Compare 0.62 and 0.59.
Both have 6 tenths, but 0.62 has 2 hundredths while 0.59 has 9 hundredths — so 0.62 is smaller.

Example 2: Arrange 0.3, 0.25, and 0.38 in order.
Line up: 0.30, 0.25, 0.38 → ascending order: 0.25, 0.3, 0.38.

Example 3: Compare 0.07 and 0.7.
Add zeros: 0.07 vs 0.70 → 0.70 is larger (7 tenths vs 0 tenths).

Example 4: Compare 0.9 and 0.95.
0.9 = 0.90 → compare hundredths → 0.95 is larger.

Common Mistakes

  • Ignoring place value: Don’t compare digits directly; compare their positions (0.45 < 0.5 even though 45 > 5).
  • Forgetting to add zeros: Always make decimals the same length before comparing.
  • Assuming more digits means a larger number: 0.9 (or 0.90) is greater than 0.89 even though it has fewer digits.

Real-Life Applications

Comparing decimals is essential for:
• Deciding which price is cheaper (£0.45 vs £0.50).
• Measuring lengths or times (0.48 m vs 0.5 m).
• Reading data from charts or digital instruments accurately.

In GCSE exams, you’ll often order decimals in ascending or descending order or compare them with fractions and percentages.

FAQs

1. What if decimals have different numbers of digits?
Add zeros until they have the same number of decimal places before comparing.

2. Are more digits always more accurate?
Yes — but not always necessary! Rounding to two decimal places is often enough for practical use.

3. How can I quickly estimate which is larger?
Compare tenths first; if they’re equal, compare hundredths. Visualising a number line also helps.

Study Tip

Practise with decimals that are close together, like 0.46 vs 0.47, or 0.89 vs 0.9. The more you practise, the faster you’ll spot which number is larger or smaller.

Mastering decimal comparison improves number sense and confidence across all GCSE Maths topics.