Reviewer for CHEMONE Finals
Rules for Counting Significant Figures
1. Nonzero integers. Nonzero integers always count as significant figures.
2. Zeros. There are three classes of zeros:
a. Leading zeros are zeros that precede all the nonzero digits. These do not count as significant figures. In the number 0.0025, the three zeros simply indicate the position of the decimal point. This number has only two significant figures.
Note that the number 1.00 _ 102 above is written in exponential notation. This type of notation has at least two advantages: the number of significant figures can be easily indicated, and fewer zeros are needed to write a very large or very small number. For example, the number 0.000060 is much more conveniently represented as 6.0 _ 10_5.
(The number has two significant figures.)
Rules for Counting Signifi cant Figures (continued)
b. Captive zeros are zeros between nonzero digits. These always count as significant figures. The number 1.008 has four significant figures.
c. Trailing zeros are zeros at the right end of the number. They are significant only if the number contains a decimal point. The number 100 has only one significant figure, whereas the number 1.00 _ 102 has three significant figures. The number one hundred written as 100. also has three significant figures.
3. Exact numbers. Many times calculations involve numbers that were not obtained using measuring devices but were determined by counting: 10 experiments,
3 apples, 8 molecules. Such numbers are called exact numbers. They can be assumed to have an infinite number of significant figures. Other examples of exact numbers are the 2 in 2_r (the circumference of a circle) and the 4 and the 3 in 43 pr3 (the volume of a sphere). Exact numbers also can arise from definitions. For example, one inch is defined as exactly 2.54 centimeters. Thus, in the statement 1 in _ 2.54 cm, neither the 2.54 nor the 1 limits the number of significant figures when used