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Significant figures, estimation and error intervals
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Good mathematicians check their answers with a quick estimate. Rounding also tells you how accurate a measurement really is.
Significant figures
The first significant figure is the first non-zero digit.
38 472 to 3 s.f. is 38 500 (keep the place value with zeros).
0.046 82 to 2 s.f. is 0.047 (the zeros at the front do not count).
38 472 to 3 s.f. is 38 500 (keep the place value with zeros).
0.046 82 to 2 s.f. is 0.047 (the zeros at the front do not count).
Estimating
Round every number to 1 significant figure, then calculate.
49.8 × 3.10.52 ≈ 50 × 30.5 = 1500.5 = 300
Use an estimate to check a calculator answer.
49.8 × 3.10.52 ≈ 50 × 30.5 = 1500.5 = 300
Use an estimate to check a calculator answer.
Error intervals
A length is 7.4 cm to 1 decimal place. The true length could be anything that rounds to 7.4.
Smallest: 7.35. It must be less than 7.45.
Error interval: 7.35 ≤ l < 7.45.
When you use a calculator, round the answer sensibly for the context: money to 2 decimal places.
Smallest: 7.35. It must be less than 7.45.
Error interval: 7.35 ≤ l < 7.45.
When you use a calculator, round the answer sensibly for the context: money to 2 decimal places.
A field is 60 m long, to the nearest 10 m. Write the error interval for its length l.
- Half of 10 m is 5 m
- Lower bound: 60 − 5 = 55. Upper bound: 60 + 5 = 65
Answer: 55 ≤ l < 65
Round to significant figures from the first non-zero digit. Estimate by rounding to 1 s.f. An error interval goes from half a unit below to half a unit above.
Check you have got it
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