Significant Figures
July 9, 2025
Introduction
Significant figures (or significant digits) are the digits in a number that carry meaning contributing to its precision. They are used in measurements and calculations to reflect the accuracy of the measuring instrument or method.
We will be determining the significant figures of some number using established rules below:
Nonzero digits are always significant
- 27 has 2 significant figures.
- 134 has 3 significant figures.
- 9.81 has 3 significant figures.
- 6.283 has 4 significant figures.
- 1.4142 has 5 significant figures.
All zeros that are found between nonzero digits are significant.
- 101 has 3 significant figures.
- 4.07 has 3 significant figures.
- 8003 has 4 significant figures.
- 20.05 has 4 significant figures.
- 60.0907 has 6 significant figures.
Leading zeros (to the left of the first nonzero digit) are not significant).
- 0.3 has 1 significant figures.
- 0.045 has 2 significant figures.
- 0.0067 has 2 significant figures.
- 0.00082 has 2 significant figures.
- 0.095 has 2 significant figures.
Zeros to the right of a non-zero digit are only significant if a decimal point is present.
- 40.2 has 3 significant figures.
- 500.1 has 2 significant figures.
- 3200 has 2 significant figures. (since there is no decimal point)
- 700000 has 1 significant figures. (since there is no decimal point)
- 10.34 has 4 significant figures.
Trailing zeros in decimal numbers are significant.
- 27 has 3 significant figures.
- 134 has 3 significant figures.
- 9.81 has 5 significant figures.
- 6.283 has 4 significant figures.
- 1.4142 has 5 significant figures.
Exact and irrational numbers have infinite significant figures.
- Exact values, such as counting numbers (e.g., 12 students), are considered to have an infinite number of significant figures.
- Constants like \pi, \, e, \text{ and }\sqrt{2} are irrational numbers and also possess an infinite number of significant figures.
- No rounding is applied when using exact or irrational values in calculations - they do not limit the number of significant figures.
Only the coefficient in scientific notation determines significant figures.
In a number expressed as A\times 10^x , only the digits in A are used to count significant figures. This means that we need to use all previous significant figure rules when analyzing A, and ignore 10^x for counting purposes.
- The exponent x only tells us the scale (magnitude) of the number and is considered exact - it does not affect the count of significant figures.
- Example: 3.20 \times 10^5 has significant figures (from 3.20).
- Example: 7.000 \times 10^{-3} \text{ has } 4 significant figures (from 7.000).