3.2. Unit Conversions, Error, and Uncertainty http://www.ck12.org
23.8 students, as there is no such thing as 8 tenths of a student. So the 24 is an exact quantity. Exact quantities
are considered to have an infinite number of significant figures; the importance of this concept will be seen later
when we begin looking at how significant figures are dealt with during calculations. Numbers in many conversion
factors, especially for simple unit conversions, are also exact quantities and have infinite significant figures. There
are exactly 100 centimeters in 1 meter and exactly 60 seconds in 1 minute. Those values are definitions and are not
the result of a measurement.
Adding and Subtracting Significant Figures
The sum or difference is determined by the smallest number of significant figures to the right of the decimal point in
any of the original numbers.
Example 3.13
- 332 + 1. 1 = 90 .432 round to 90. 4
Example 3.14
- 097 − 0. 12 = 1 .977 round to 1. 98
Multiplying and Dividing Significant Figures
The number of significant figures in the final product or quotient is equal to the number of significant figures in the
starting value that has the fewest significant figures.
Example 3.15
- 8 × 4. 5039 = 12 .61092 round to 13
Example 3.16
- 85 ÷ 112. 04 = 0 .0611388789 round to 0. 0611
Example 3.17
For this example, the value 8 is known to be exact (so it has an infinite number of significant figures).
- 2786 × 8 = 2. 229
Calculating Density
Imagine holding a tennis ball in one hand and an orange in the other. Why does the orange feel heavier than the
tennis ball, even though the two objects are about the same size? This can be explained with the concept ofdensity.
Density is an expression of the mass of a substance in terms of the volume occupied by the substance. The equation
for density is:
Density=
mass
volume
D=
m
V
So, even though a tennis ball and an orange may be about the same volume, the orange contains more mass within
that volume than does the tennis ball. Therefore, the orange has a higher density. This is because the orange contains
mostly water and the tennis ball contains mostly air; as you might imagine, water is much heavier than air.
Density is typically reported in terms of gram per milliliter (g/mL) or the equivalent value, grams per cubic centime-
ter (g/cm^3 ). Oftentimes, scientists compare the density of an object to the density of water which is 1 g/mL at room