Significant figures

Significant figures (also known as the significant digits, precision or resolution) of a number in positional notation are digits in the number that are reliable and necessary to indicate the quantity of something. If a number expressing the result of a measurement (e.g., length, pressure, volume, or mass) has more digits than the number of digits allowed by the measurement resolution, then only as many digits as allowed by the measurement resolution are reliable, and so only these can be significant figures. For example, if a length measurement gives 114.8 mm while the smallest interval between marks on the ruler used in the measurement is 1 mm, then the first three digits (1, 1, and 4, showing 114 mm) are certain and so they are significant figures. Digits which are uncertain but reliable are also considered significant figures. In this example, the last digit (8, which adds 0.8 mm) is also considered a significant figure even though there is uncertainty in it. Another example is a volume measurement of 2.98 L with an uncertainty of ± 0.05 L. The actual volume is somewhere between 2.93 L and 3.03 L. Even when some of the digits are not certain, as long as they are reliable, they are considered significant because they indicate the actual volume within the acceptable degree of uncertainty. In this example the actual volume might be 2.94 L or might instead be 3.02 L. And so all three are significant figures. The following digits are not significant figures. All leading zeros. For example, 013 kg has two significant figures, 1 and 3, and the leading zero is not significant since it is not necessary to indicate the mass; 013 kg = 13 kg so 0 is not necessary. In the case of 0.056 m there are two insignificant leading zeros since 0.056 m = 56 mm and so the leading zeros are not necessary to indicate the length. Trailing zeros when they are merely placeholders. For example, the trailing zeros in 1500 m as a length measurement are not significant if they are just placeholders for ones and tens places (supposing the measurement resolution is 100 m).