Significant figures ("sig figs") is the number of digits that carry precision in a number.
Non-measured numbers, such as π, integer counts, definition of units, etc. always have infinite sig figs. Other constants, such as NA, have limited sig figs.
Nonzero digits are always significant, unless one or more of the other rules are violated.
Leading zeros are never significant; trailing zeros, however, are significant only if they are part of the measurement. Zeros between non-zero digits are always significant.
Reported numbers are only significant to the precision of the equipments with which they are measured.
When adding or subtracting two numbers, the result should have as many decimal places as the number with the smallest sig figs.
When multiplying or dividing, the result should have as many sig figs as the number with the smallest sig figs.
Logarithms use the number of significant digits in the input as the result's number of decimals (mantissa).
For example, in
log(123) = 2.090, the input has three sig figs, and the output (after rounding) has 3 decimal places.
Anti-Logarithms are the opposite of logarithms, and also have the opposite rule: the number of significant digits in the result is equal to the number of decimal places in the power.
For example, reversing the previous example we get:
102.090 = 123. The power has three decimal places and the output (after rounding) has 3 significant digits.
You can use our online significant figure calculator to evaluate expressions using any of the above operations.