How to Identify the Significant Figures in Calculations

Label any non-zero digit that appears in a number as being significant. Use the number 3.568 as an example, and note that there are 4 significant digits in this number because there are no zeros.

Label zeros that appear to the left of a decimal point as insignificant, such as the zero in 0.423. Label zeros that appear between numbers as significant, such as the zero in 4.203. Label zeros that appear to the right of a decimal point, before other digits, as insignificant because they are placeholders for the decimal (example: 0.0002 only has 1 significant figure) and can be eliminated by writing in scientific notation (0.0002 becomes 2 x 10^-4). Label zeros that appear to the right of the other digits in a decimal (called trailing zeros) as significant, such as in 5.380, because they represent the accuracy to which the decimal was measured.

Note that zeros at the end of a number may be significant or insignificant depending on the situation. Determining which it is depends on the algebraic operation that produced the answer. Addition and subtraction solutions round the answer to significant figures equal to the number of decimal places in the smaller original number while in multiplication and division, the solution should be rounded so it has the same number of significant figures as the number of significant figures in the smaller original number. Writing the resulting digits in scientific notation makes it easier to determine the number of significant figures: 50, 600 with 3 significant figures becomes 5.06 x 10^4.