Significant Figures
Goals:
1. To learn to determine the number of significant figures in a number.
2. To learn the use of significant figures correctly in calculations.
3. To learn to use scientific notation.
Determining the number of significant figures (S.F.) in a number:
Measure numbers always contain error. Numbers obtained by counting or defined numbers are exact. For example 28 students in a classroom is an exact number. 12 inches in one foot is defined and is also exact. An exact number has an infinite number of significant figures. The number of significant figures in a measured number is limited by the measuring device used.
Rules for Counting Significant Figures: Example # S.F.
1. All nonzero integers are significant. 421.1 4
2. Leading zeros are never significant. 0.0034 2
3. Captive zeros are always significant. 205 3
4. Trailing zeros in a decimal number are significant. 25.0 3
5. Trailing zeros in a number with no decimal are not significant. 400 1
Scientific Notation:
The number of significant figures in a number written in exponential notation is easily determined as the leading and trailing zeros are removed.
Examples:
Decimal Scientific Notation # S.F.
0.0034 3.4 x 10 -3 2
400 4 x 10 2 1
0.000505 5.05 x 10 -4 3
530000 5.3 x 10 5 2
0.0100 1.00 x 10 -2 3
(0.0100 contains trailing zeros within a decimal.)
Rules for Rounding:
1. In a calculation carry all of the significant figures through to the final result, then round.
2. If the digit t be removed is <5, the preceding digit remains unchanged. 25.44 rounds to 25.4
3. If the digit to be removed is > or = 5, then the preceding digit is increased by 1. 25.46 rounds to 25.5