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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.

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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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