The idea of significant figures (commonly called sig figs) is a method of expressing error in measurement. When the number of significant figures increase, the measurement becomes more exact.

Significant figures conventionally follow certain sets of rules:

• All non-zero digits are significant: for example, 87.636 has five significant figures.
• Any zeros that are between non-zeros are considered significant; for example, 40.02 has four significant figures.
• Any zeros that follow the decimal place in numbers smaller than one are not considered significant, e.g., 0.00057 has two significant figures.
• Any zeros that follow the last non-zero digit to the right of the decimal point are significant, e.g.: 0.002400 has four significant figures and 90 has one significant figure.

Conventionally, a number with value 0 is considered to have one significant figure, yet a number with value 0.0000 has an exponent of -4, but only one significant figure.

In order to indicate exactly which digits are significant, values such as two thousand should be expressed in scientific notation, if necessary, using the correct number of significant figures. If only two digits — the '2' and the first '0' — are significant (i.e., the true value could be anywhere from 1950 to 2049), the appropriate representation is 2.0 x 10³; if three are significant (the value is in the range 1995 to 2004) then it is 2.00 x 10³; if four are significant (from 1999.5 to 2000.4), then it could be either 2000 (two, zero, zero, zero) or 2.000 x 10³. (For clarity, the former form could be written 2000., with a decimal point; otherwise, some may read the number as having just one significant digit and three zeros for placement.) If five, it could be either 2000.0 or 2.0000 x 10³.

The same can be achieved by using another unit for the quantity expressed. A distance of 2000 m is supposed to have four significant digits, but 2 km has only one. More informally it can be done by using words to express numbers. The value 12 million has two significant digits, while officially 12,000,000 has 8. In practical situations it is wise to consider multiple trailing zeroes as insignificant.

Sometimes a bar over a trailing zero is used to indicate that it is significant. For example, appears to have four significant digits; the bar indicates that in fact the second zero is the last significant digit.

When dealing with significant figures in calculations, follow these rules:

For multiplication and division, round your final answer to the least number of sig figs used in any of the terms:

The answer is rounded to three sig figs, because the least number of sig figs in our equation was 4.87 which has 3 sig figs. The other numbers, 15.03 and 1.987, have 4 significant figures each.

For addition and subtraction, you will round your final answer to the least number of decimal places, not the least number of sig figs of any one term:

The answer is rounded to two decimal places, because 13.45 is the term with the smallest number of decimal places.

If the problem contains more than one mathematical operation:

Perform the subtraction first to determine how many sig figs will be in the numerator:

The subtraction results in a number with two decimal places, so the least number of sig figs for the multiplication and division is two sig figs and the final answer will be rounded to two sig figs.