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.
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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
Convert all to decimals: 0.35 = 0.35, 3/8 = 0.375, 0.3 = 0.3, 2/5 = 0.4
Order the decimals: 0.3, 0.35, 0.375, 0.4
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
Plot on a number line mentally: −3, −1.5, −0.2, 0.5
Largest to smallest means right to left on the number line
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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