Overview

Significant Figures are the significant number of digits used to take measurements or used in calculations. Most digits are actually significant. Zero is the only digit that is not significant. They are only used to position the decimal points.

There are three steps needed to satisfy significant figures.
1. The measured quantity must have a decimal point
2. Start left, then move right to the first nonzero digit
3. That digit must be counted and every digit to its right is considered significant

Complication

Zeros that end a number & lie either before or after the decimal points are considered significant.

Examples of Significant Figures

4 significant figures
5.080 kM
9820. kM
5.080 x 10^3 M

3 significant figures
3.00 x 10^2 mL
900. mL
0.300 L

2 significant figures
9800 mL
5.90 x 10^3 L

1 significant figure
500 mL
4 L

Significant Figures in Calculations

Many times there are too many significant figures, so we round off the answer to get the proper number of them.
The least measurement usually sets the limit for the entire calculation which determines the number of significant figures in the final answer.

Significant Figures in Arithmetic Operations

1. Multiplication & Division
The answer has the same amount of significant figures as the measurement with the fewest significant figures.

Example: 2 mL x 4.3 mL x 22.29 mL = 2 x 10^2 mL
2000. mL / 10. = 20. X 10^1 mL

2. Addition & Subtraction
The answer has the same amount of significant figures as there are in the measurement with the fewest decimal place.

Example: 22.2 mL + 22.22 mL = 44. 4 mL
23.2 mL – 10.00 mL = 13.2 mL

Rounding Off Rules

1. If the number is >5, the next number increases by 1.
986.567 rounds to 986.57 for 5 significant figures or 985.6 for 4 significant figures.

2. If the number is <5, the next number stays the same.
.2921 rounds to .292 for 3 significant figures or .29 for 2 significant figures.

3. If the number is =5, the next number increase by 1 if it is odd and stays the same if it is even.
18.75 rounds to 18.8, but 18.65 rounds to 18.6

4. One or more additional significant figures must be carried throughout calculations. Only final answer should be rounded.

Exact Numbers

Exact numbers have no uncertainty and many times are constants.
They do not limit the number of significant figures in the answer.
Many times the exact number will have as many significant figures as the calculation is required.

Example: 48 hours in 1 day. 60 minutes in 1 hour. 60 seconds in 1 minute. 26 letters in the English alphabet.

Resources

Silberberg, Martin S. Principles of General Chemistry. Boston: McGraw-Hill Higher Education, 2007. Print.