1.1 – Measurements in physics
Significant figures
Calculators usually give you many digits in an answer. How do you decide how many digits to write down for the final answer?
Scientists use a method of rounding to a certain number of significant figures (often abbreviated to s.f.). “Significant” here means meaningful. Some rules for using significant figures are:
- A digit that is not a zero will always be significant – 345 is three significant figures (3 s.f.).
- Zeros that occur sandwiched between non-zero digits are always significant – 3405 (4 s.f.); 10.3405 (6 s.f.).
- Non-sandwiched zeros that occur to the left of a non-zero digit are not significant – 0.345 (3 s.f); 0.034 (2 s.f.).
- Zeros that occur to the right of the decimal point are significant, provided that they are to the right of a non-zero digit – 1.034 (4 s.f.); 1.00 (3 s.f.); 0.34500 (5 s.f.); 0.003 (1 s.f.).
- When there is no decimal point, trailing zeros are not significant (to make them significant there needs to be a decimal point) – 400 (1 s.f.); 400. (3 s.f.) – but this is rarely written.
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