The following lesson is one lecture in a series of Chemistry Programs developed by Professor Larry Byrd Department of Chemistry Western Kentucky University

PART 3 Significant Figures

We can easily see why 36 mL has two significant figures; 36.8 mL has three significant figures, and 4536 meters has four significant figures. However, a problem arises when a zero is found in a reported measurement. The placement of the zero in a number will determine whether or not the zero is significant.

The following rules will be used to determine the number of significant figures found in a measurement: 1. All recorded nonzero numbers are "always" significant figures. The numbers 1, 2, 3…, through 9 are all nonzero numbers and therefore, are all significant figures.

2.All zeros are significant if they are located "between" two nonzero numbers: has four significant figures 606 has three significant figures has four significant figures 6.06 has three significant figures 2004 has four significant figures10.6 has three significant figures The following rules will be used to determine the number of significant figures found in a measurement:

3.All zeros to the RIGHT of a nonzero number after a decimal point are significant: has three significant figures (the "7", "0", and "0") 1.00 has three significant figures (the "1", "0", and "0") has five significant figures (the "6", "4", "1", "7", and "0") The following rules will be used to determine the number of significant figures found in a measurement:

4. A zero is not significant when it is used only to mark the position of the decimal point in a number less than one: a. 0.2 has one significant figure (the "2"). However, if a number in chemistry is less than one "it" must always be written in scientific notation! All numbers in front of the times symbol, which are known as the first part, are significant figures: In this example, 0.2 = 2 X when it is written in Scientific Notation, it can be easily seen that there is only one significant figure! The following rules will be used to determine the number of significant figures found in a measurement:

4. A zero is not significant when it is used only to mark the position of the decimal point in a number less than one: b has three significant figures (the "2", "0", and "5"). Since = 2.05 X in scientific notation; thus, three significant figures. The following rules will be used to determine the number of significant figures found in a measurement:

4. A zero is not significant when it is used only to mark the position of the decimal point in a number less than one: c has three significant figures (the "1", "2",and "3") Since = 1.23 X in scientific notation; thus, three significant figures. The following rules will be used to determine the number of significant figures found in a measurement:

4. A zero is not significant when it is used only to mark the position of the decimal point in a number less than one: d has four significant figures (the “1", “2", “3" and “0") Since = X in scientific notation; thus, four significant figures. The following rules will be used to determine the number of significant figures found in a measurement:

5.The zeros to the right of nonzero numbers, but before the decimal point may or may not be significant. For example, if an announcer at a basketball game says the attendance is 100, we would probably be correct in assuming that it is only an estimated value and there is only one significant figure present. The following rules will be used to determine the number of significant figures found in a measurement:

However, if we were reading a report that states that 100. germs were found in a sample, then we must assume that the scientist placed the decimal point after the last zero to show us that actually there were 100. germs present. Thus, the 100. contains three significant figures. 5.The zeros to the right of nonzero numbers, but before the decimal point may or may not be significant. The following rules will be used to determine the number of significant figures found in a measurement:

100. germs germs Fair MethodBest Method The best way to report the germ count would have been to give its value in scientific notation and include all the zeros to show that they are all significant: 5.The zeros to the right of nonzero numbers, but before the decimal point may or may not be significant. The following rules will be used to determine the number of significant figures found in a measurement:

Value recorded as Number of Significant Figures x x x The number 200 may have one, two, or three significant figures depending upon how accurate the measurements were made: 5.The zeros to the right of nonzero numbers, but before the decimal point may or may not be significant. The following rules will be used to determine the number of significant figures found in a measurement:

In summary of rule (5): If a measurement's reported value ends in a zero and a decimal point is used, then the value should be given in scientific notation so that the reader will know how accurate the measurement was made. Table 1 contains other examples of the number of significant figures found in measurements:

Table One: Significant Figures Measurement Number of Significant figures Measurement Number of Significant Figures 1.77 mm 3 93,000,000 miles must be written as … 9.3 x miles cm 31.0 x 10 2 people m must be… 1.07 x m 31 x 10 2 people km must be… 1.0 x km m must be… 1 x m m must be… 2 x m m must be… 1.00 x m billion people 4.5 x people 2