What Are Sig Figs?
Sig figs are the meaningful digits in a measured or calculated value. They show how much precision a number is allowed to claim.
Sig figs meaning in one sentence
Sig figs, or significant figures, are the digits in a number that communicate measurement precision: all reliable digits plus the final estimated digit.
A ruler, scale, or instrument limits how many digits you should report.
Chemistry and physics use sig figs to keep calculated answers honest.
The final answer should not be more precise than the least precise input.
How to identify sig figs
Non-zero digits count
Digits 1-9 always carry measured value, so they are significant.
Zeros between non-zero digits count
A zero trapped between measured digits is part of the reported value.
Leading zeros do not count
Zeros before the first non-zero digit only locate the decimal point.
Trailing decimal zeros count
A zero after a decimal point shows the measurement was reported to that place.
Trailing whole-number zeros can be ambiguous
Use scientific notation when you need to show whether the zeros are measured.
Examples of sig figs
| Number | Sig figs | Why |
|---|---|---|
| 0.00450 | 3 | 4 and 5 count, and the final decimal zero shows precision. |
| 100 | 1 by default | The zeros are placeholders unless notation or context says otherwise. |
| 100.0 | 4 | The decimal point makes the trailing zeros significant. |
| 3.20 x 10^4 | 3 | Only the coefficient 3.20 controls the sig fig count. |
| 12 eggs | exact | Counted items are exact numbers, so they do not limit calculation precision. |
Sig figs vs decimal places
Sig figs
Count meaningful digits from the first non-zero digit. In 0.00450, the sig figs are 4, 5, and the final 0.
Decimal places
Count positions after the decimal point. In 0.00450, there are 5 decimal places, but only 3 significant figures.
Common mistakes
Counting leading zeros in small decimals such as 0.0045.
Dropping a trailing decimal zero when it shows precision, such as changing 2.50 to 2.5.
Treating 100, 100., and 1.00 x 10^2 as if they communicate the same precision.
Using sig fig rules for addition when the calculation requires decimal-place rules.
Frequently asked questions
What are sig figs?
Sig figs, short for significant figures, are the digits in a measured or calculated number that show meaningful precision. They include all certain digits plus the final estimated digit.
Why do sig figs matter?
Sig figs keep an answer from claiming more precision than the original measurements support. This is why they are used in chemistry, physics, engineering, and lab reports.
Are sig figs the same as decimal places?
No. Sig figs count meaningful digits starting with the first non-zero digit. Decimal places count fixed positions after the decimal point.
Do leading zeros count as sig figs?
No. Leading zeros do not count because they only place the decimal point. In 0.0045, only 4 and 5 are significant.
Do exact numbers have sig figs?
Exact numbers are treated as having unlimited significant figures. Counted objects and defined conversions, such as 12 eggs or 100 cm in 1 m, do not limit the precision of a calculation.