Using Significant Figures
The significant figures in a decimal are the digits that are
warranted by the accuracy of a measuring device.
When you perform a calculation with measurements, the number of significant
figures to include in the result depends in part on the number of significant
figures in the measurements. When you multiply or divide measurements, your
answer should have only as many significant figures as the measurement with
the fewest significant figures.
Example
Using a balance and a graduated cylinder filled with water, you determined that a marble has a mass of 8.0 grams and a volume of 3.5 cubic centimeters. To calculate the
density of the marble, divide the mass by the volume.
mass
Volume
Write the formula for density: Density = 8.0 g
3
Substitute measurements:
=
Use a calculator to divide:
⬇ 2.285714286 g/cm3
3.5 cm
MATH HANDBOOK
ANSWER Because the mass and the volume have two significant figures each,
give the density to two significant figures. The marble has a density of 2.3 grams
per cubic centimeter.
Using Scientific Notation
Scientific notation is a shorthand way to write very large or very
small numbers. For example, 73,500,000,000,000,000,000,000 kg is the
mass of the Moon. In scientific notation, it is 7.35 ⴛ 1022 kg.
Example
You can convert from standard form to scientific notation.
Standard Form
Scientific Notation
720,000
7.2 105
5 decimal places left
Exponent is 5.
0.000291
2.91 10–4
4 decimal places right
Exponent is –4.
You can convert from scientific notation to standard form.
R44 Student Resources
Scientific Notation
Standard Form
4.63 46,300,000
107
Exponent is 7.
7 decimal places right
1.08 10–6
0.00000108
Exponent is –6.
6 decimal places left