How to count significant figures
- Type a number exactly as it was measured or written, including any trailing zeros and the decimal point.
- The count appears with the significant digits underlined, and the rules that applied are listed.
- To round, choose the number of significant figures in the second card. The result is shown in standard and scientific notation.
The rules for significant figures
- All non-zero digits are significant: 452 has 3.
- Zeros between non-zero digits are significant: 4,005 has 4.
- Leading zeros are never significant: 0.0045 has 2.
- Trailing zeros after a decimal point are significant: 4.50 has 3, and 0.004050 has 4.
- Trailing zeros in a whole number with no decimal point are ambiguous: 1200 may have 2, 3 or 4. Write 1200. (with a point) or 1.20 × 10³ to make the precision clear.
Significant figures express how precise a measurement is. When multiplying or dividing, round the answer to the fewest significant figures among the inputs; when adding or subtracting, round to the fewest decimal places. Rounding here uses the decimal digits as written and rounds half up, so 0.0455 to two significant figures is 0.046. When rounding a whole number such as 1,750 to 2 significant figures, the result 1,800 has placeholder zeros, so the scientific form 1.8 × 10³ is the unambiguous way to report it.
How many significant figures does 100 have?
One, by the usual convention, because trailing zeros without a decimal point are placeholders. 100. has three, and 1.00 × 10² also has three.
Are exact numbers limited by significant figures?
No. Counted quantities (12 eggs) and defined constants (100 cm in 1 m) are exact and have unlimited significant figures.
How do I round 3.14159 to 3 significant figures?
Keep the first three digits (3.14) and look at the next one (1). It is under 5, so the answer is 3.14.