Significant Figures

We often indicate the probable uncertainty associated with an experimental measurement by rounding the result so that it contains only significant figures. By definition, the significant figures in a number are all of the certain digits plus the first uncertain digit. For example, when you read the 50-mL buret section shown in Figure 1.1, you can easily tell that the liquid level is greater than 30.2 mL and less than 30.3 mL. You can also estimate the position of the liquid between the graduations to about 0.02 mL. So, using the significant figure convention, you should report the volume delivered as 30.24 mL, which has four significant figures. Note that the first three digits are certain, and the last digit (4) is uncertain.

A zero may or may not be significant depending on its location in a number. A zero that is surrounded by other digits is always significant (such as in 30.24 mL) because it is read directly and with certainty from a scale or instrument readout. On the other hand, zeros that only locate the decimal point for us are not. If we write 30.24 mL as 0.03024 L, the number of significant figures is the same. The only function of the zero before the 3 is to locate the decimal point, so it is not significant. Terminal, or final, zeros may or may not be significant. For example, if the volume of a beaker is expressed as 2.0 L, the presence of the zero tells us that the volume is known to a few tenths of a liter so that both the 2 and the zero are significant figures. If this same volume is reported as 2000 mL, the situation becomes confusing. The last two zeros are not significant because the uncertainty is still a few tenths of a liter or a few hundred milliliters. In order to follow the significant figure convention in a case such as this, use scientific notation and report the volume as 2.0 × 10³ mL.

Figure 1.1 A buret section showing the liquid level and meniscus.