1. Significant Figures Why significant figures are important
Please remember that, in science, all numbers are based upon measurements (except for a very few that are defined).
Since all measurements are uncertain, we must only use those numbers that are meaningful.
A common ruler cannot measure something to be cm long.
Not all of the digits have meaning (significance) and, therefore, should not be written down.
In science, only the numbers that have significance (derived from measurement) are written.

2. Significant Figures
There are two rules for determining the number of significant figures
Note: significant figures is abbreviated sig. figs.

3. Significant Figures Rule 1 If there is no decimal point
Start at the RIGHT
Count, beginning with the first non-zero digit.
Examples
sig.figs.
sig.figs.
sig.figs.

4. Significant Figures Rule 2 If there is a decimal point
Start at the LEFT
Count, beginning with the first non-zero digit.
Examples
sig.figs.
sig.figs.
sig.figs.
sig.figs.

5. Significant Figures
There are two rules for determining the number of significant figures to display in a reported number

6. Significant Figures When you multiply and/or divide
Count the sig. figs. in the numbers you are multiplying and/or dividing.
Your answer should be rounded off to the smallest number of sig. figs. in your problem. Examples
28.33 x 3.12 (4 sig.figs. and 3 sig. figs., respectively)
calculator answer
reported answer (must have 3 sig. figs.)    
28.44 x 3.12 (4 sig.figs. and 3 sig. figs., respectively)
calculator answer
reported answer (must have 3 sig. figs.)
Reminder: Rounding-off rules: Go to next number. If it is 0-4, round down. If it is 5-9, round up

7. Significant Figures When you add and/or subtract
Count the sig. figs. in the numbers you are adding and/or subtracting
The answer should have the same number of decimal places as that of the number with the least number of decimals.
Examples
4.838 g g =  g
Only 3 digits to right of decimal are allowed
4th decimal to right, 3, is 0-4, so round down
5.385 is reported answer
g g = g
No digits to right of decimal are allowed
1st decimal to right, 5 is 5-9, so round up
66 g reported answer
Reminder: In addition and subtraction, decimals must be lined up

8. Significant Figures
Complete the significant figures worksheet