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- Rounding and estimation
Rounding and estimation
Rounding gives a sensible answer; estimating checks whether a calculator answer is believable.
Decimal places and significant figures
Decimal places count digits after the point. 3.476 to 1 d.p. is 3.5.
Significant figures count from the first non-zero digit. 0.04071 to 2 s.f. is 0.041.
Look at the next digit: 5 or more rounds up.
Significant figures count from the first non-zero digit. 0.04071 to 2 s.f. is 0.041.
Look at the next digit: 5 or more rounds up.
Estimating
Round every number to 1 significant figure, then work it out.
48.7 × 3.10.52 ≈ 50 × 30.5 = 1500.5 = 300
48.7 × 3.10.52 ≈ 50 × 30.5 = 1500.5 = 300
Error intervals
If a length is 7.3 cm to 1 d.p., the real value could be anywhere from 7.25 up to (but not including) 7.35.
7.25 ≤ x < 7.35
7.25 ≤ x < 7.35
Estimate 612 × 0.198
- Round to 1 s.f.: 600 × 0.2
- = 120
Answer: About 120
Significant figures start at the first non-zero digit. Estimate by rounding each number to 1 s.f. An error interval runs from half a unit below to half a unit above.
Check you have got it
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