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

Rounding & significant figures

Rounding makes numbers easier to work with. You need to round to a given number of decimal places (dp) or significant figures (sf). Look at the digit after the one you keep: 5 or more rounds up, 4 or less stays the same.

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Key facts to remember

  • 1Decimal places count digits after the decimal point.
  • 2Significant figures count digits starting from the first non-zero digit.
  • 3If the next digit is 5, 6, 7, 8 or 9 → round up.
  • 4If the next digit is 0, 1, 2, 3 or 4 → round down (leave the digit alone).
  • 5Trailing zeros in a decimal (e.g. 2.30) are significant.
  • 6Leading zeros (e.g. 0.0073) are NOT significant.
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Worked examples

Example 1

Round 7.4683 to 2 decimal places.

Working

  1. Identify the 2nd decimal place: 7.46|83
  2. Look at the next digit: 8 → round up
  3. 6 becomes 7
Answer7.47
Example 2

Round 0.004927 to 2 significant figures.

Working

  1. First sig fig is 4 (leading zeros do not count).
  2. 2nd sig fig is 9. Next digit is 2 → round down.
  3. 0.0049
Answer0.0049
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Common mistakes

✗Counting leading zeros as significant figures.
✗Rounding prematurely in multi-step calculations — round at the final step only.
✗Forgetting to keep trailing zeros (e.g. writing 2.3 instead of 2.30 when rounding to 2 dp).
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Exam tips

✓Read carefully: "to 2 dp" and "to 2 sf" give different answers.
✓When asked for a "sensible degree of accuracy", use 3 sf for calculator answers.
✓Keep full accuracy in your calculator, then round at the very end.

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