# Significant Figures

Significant figures ("sig figs") is the number of digits that carry precision in a number.

## Non-measured Numbers

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.

## Non-zero Digits

Nonzero digits are always significant, unless one or more of the other rules are violated.

## Zeros

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.

## Reporting Numbers

Reported numbers are only significant to the precision of the equipments with which they are measured.

## Addition/Subtraction

When adding or subtracting two numbers, the result should have as many decimal places as the number with the smallest sig figs.

## Multiplication/Division

When multiplying or dividing, the result should have as many sig figs as the number with the smallest sig figs.

## Logarithms

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

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.

## Performing Calculations

You can use our online significant figure calculator to evaluate expressions using any of the above operations.