Units, Scientific Notation, and Significant Figures

Significant Figures

For example, let's say you have to add the numbers 1.121, 48.00679392, and 6.3457:

1.121 + 48.00679392 + 6.3457 = 55.47349392
But, because 1.121 has only three decimal places, the answer must actually be: 55.473, since it is at the third decimal place that uncertainty begins to enter the picture.

Significant Figures in Multiplication and Division

The rule governing multiplication and division of significant figures is slightly different than that for addition and subtraction, but just as simple:

The final value can only have as many significant figures as the original value with the least significant figures.

For example, consider the following situation: a scientist needs to calculate a constant value, K, based on the following equation:

K = (D x E) / B
where B, D and E are measured values that the scientist observed (weight, volume, temperature, pressure).

B=6.00 g D= 22 C E= 22.457 mL

22.457 mL has 5 significant figures and 22 C has 2 significant figures. The number that the calculator gives is 82.34233... However this has 7 significant figures and none of the measurements were this accurate. In fact, we must reduce the answer to only two significant figures, since that's how many 22 has. The answer, K, must be truncated to 82 ml C/g to reflect the 2 significant figures in the D value.

From the SparkNotes Blog