Significant Figures
General Rules for Significant Figures
1. Any digit that is not zero is significant
2. Zeros between non zero digits are significant
3. Zeros to the left of the first non zero digit are not significant. They just indicate the position of the decimal.
4. If a number is greater than 1, then all the zeros to the left of the decimal point are significant as long as the decimal point is written. If the decimal point is not written, they are not significant. (Best way to avoid confusion is to use scientific notation.)
5. For numbers that contain a decimal, any zeros written to the right are significant.
6. For numbers in Scientific Notation, all the digits written are significant.
7. Exact numbers from definitions or by counting objects have an infinite number of significant digits. Watch the units.
18 people has an infinite number of sig figs.
The conversion, 12 inches in 1 foot is exact, so it has an infinite number of sig figs.
22 inches is a measurement (not a conversion) and therefore has only 2 sig figs.
Handling Significant Figures in Calculations:
1. Addition and Subtraction
The number of digits to the right of the decimal is determined by the original numbers that had the lowest number of digits to the right of the decimal. (i.e. take the first complete column of numbers from the right.)
45.789 + 3.4 = 46.189, rounded off to 46.2**
** when rounding off, if the next digit is 5 or more, round up. if the digit is 4 or less, leave the preceding digit as is.
2. Multiplication and Division
The number of significant digits in the answer is equal to the smallest number of significant digits in the original numbers.
If you multiply 3.4 x 0.982 x 9000., your answer should have just 2 sig figs. (3.4 has 2, 0.982 has 3, and 9000. has four)