Rules for counting significant Figures  (MISC)


1. Nonzero integers. Nonzero integers always count as significant fig­ures. For example, the number 1457 has four nonzero integers, all of which count as significant figures.

2. Zeros. There are three classes of zeros:

a. Leading zeros are zeros that precede all of the nonzero digits. They never count as significant figures. For example, in the number 0.0025, the three zeros simply indicate the position of the decimal point. The number has only two significant figures, the 2 and the 5.

b. Captive zeros are zeros that fall between nonzero digits. They al­ways count as significant figures. For example, 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 is written with a decimal point. The number one hundred written as 100 has only one significant figure, but written as 100., it has three significant figures.

3. Exact numbers. Often 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 unlimited number of significant figures. Exact numbers can also arise from definitions. For example, 1 inch is defined as exactly 2.54 centimeters. Thus in the statement 1 in. = 2.54 cm, neither 2.54 nor 1 limits the number of significant fig­ures when it is used in a calculation.


You will find this chart at the bottom of page 25 and top of page 26 in your textbook.