GCSE Maths Rounding & Estimation Notes
Rounding makes numbers simpler while keeping them close to the original value. Estimation and bounds let you check answers and quantify accuracy.
Key concepts
- Decimal places (d.p.)
- Count digits after the decimal point. Look at the next digit: 5 or more rounds up, less than 5 rounds down.
- Significant figures (s.f.)
- The first non-zero digit is the 1st significant figure. Zeros between digits count; leading zeros do not.
- Estimation
- Round every number to 1 significant figure, then calculate — a fast way to check a calculator answer is sensible.
- Upper & lower bounds
- A rounded value could come from a range. Half a unit either side gives the bounds (error interval).
Key formulas
Error interval
lower bound ≤ x < upper bound
For a value rounded to the nearest unit, add/subtract half that unit.
Worked example
Estimate 38.6 × 5.13 ÷ 1.94.
- 1Round each number to 1 significant figure: 40, 5 and 2.
- 2Calculate 40 × 5 = 200.
- 3Divide by 2: 200 ÷ 2 = 100.
Answer: ≈ 100 (calculator value ≈ 102.1)
Common mistakes
✗ Counting leading zeros as significant, e.g. 0.0047 to 1 s.f. giving 0.00.
✓ The first significant figure is the first non-zero digit — 0.0047 to 1 s.f. is 0.005.
✗ Rounding 3.548 to 2 d.p. as 3.54.
✓ The third decimal (8) rounds the 4 up: 3.55.
✗ Writing the error interval with ≤ on both ends.
✓ Use ≤ lower bound and < upper bound, e.g. 24.5 ≤ x < 25.5.
Quick check
Try these, then reveal the answers.
Round 6.749 to 1 d.p.Reveal answer
6.7
Round 0.03086 to 2 s.f.Reveal answer
0.031
A length is 12 cm to the nearest cm. Give the error interval.Reveal answer
11.5 ≤ x < 12.5
Exam tips
- Estimation questions want rounding to 1 s.f. — show the rounded numbers to earn the method mark.
- For bounds problems, use the largest values for a maximum and the smallest for a minimum.
- Never round part-way through a multi-step calculation; round only the final answer.
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Frequently asked questions
What is the difference between decimal places and significant figures?+
Decimal places count digits after the point; significant figures count from the first non-zero digit, wherever it appears.
Why do we estimate if we have a calculator?+
Estimation checks that a calculator answer is the right size, catching key-press errors that would otherwise go unnoticed.
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