EST. 2024 · LONDON·MMXXVI SPECIFICATION
AQA·Edexcel·OCR|Foundation + Higher
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Number · Foundation & Higher

Ordering & comparing numbers

Ordering numbers means arranging them from smallest to largest (or vice versa), including integers, decimals, fractions and negative numbers. Comparing numbers requires understanding place value and number lines.

Revising ordering & comparing numbers the night before an exam? These are condensed revision notes — the facts, formulas and mistakes examiners actually mark, with no long explanations. Prefer a full walkthrough with step-by-step reasoning instead? Search “Ordering & comparing numbers GCSE” on the site for the complete guide.

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Key facts to remember

  • 1Negative numbers: the further from zero, the smaller the value (e.g. −7 < −2).
  • 2To compare decimals, line up the decimal points and compare digit by digit.
  • 3To compare fractions, convert to a common denominator or to decimals.
  • 4Place value: each digit's value depends on its position (ones, tens, hundreds, tenths, hundredths…).
  • 5On a number line, numbers increase from left to right.
  • 6Inequality symbols: < means "less than", > means "greater than", ≤ means "less than or equal to".
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Worked examples

Example 1

Write these numbers in order from smallest to largest: 0.35, 3/8, 0.3, 2/5

Working

  1. Convert all to decimals: 0.35 = 0.35, 3/8 = 0.375, 0.3 = 0.3, 2/5 = 0.4
  2. Order the decimals: 0.3, 0.35, 0.375, 0.4
  3. Convert back to original form: 0.3, 0.35, 3/8, 2/5
Answer0.3, 0.35, 3/8, 2/5
Example 2

Write these numbers in order from largest to smallest: −1.5, −3, 0.5, −0.2

Working

  1. Plot on a number line mentally: −3, −1.5, −0.2, 0.5
  2. Largest to smallest means right to left on the number line
  3. Order: 0.5, −0.2, −1.5, −3
Answer0.5, −0.2, −1.5, −3
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Common mistakes

✗Thinking −7 > −2 because 7 > 2 — with negatives, the larger the digit, the smaller the value.
✗Comparing decimals by length rather than place value (e.g. thinking 0.35 > 0.4 because it has more digits).
✗Not converting fractions to the same form before ordering.
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Exam tips

✓Convert everything to decimals before ordering — it's the easiest common format to compare.
✓Draw a quick number line if you're unsure about negative numbers.

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