1. Significant Figures Notes
Sig Figs for short

2. What is a sig fig?
All numbers of a measured quantity, including an estimated one.
It has to do with precision. The more numbers past the decimal point, the more precise the measurement.

3. 5 Rules 1. All nonzero digits are significant. Example: 1234
(4 sig figs)
2. Zeros between nonzero digits are significant.
Example: 1005

4. 5 Rules 3. All leading zeros are NOT significant. Example: 0.000078
(2 sig figs)
4. All trailing zeros (behind the decimal point) are significant. If there is not a decimal point in a number, trailing zeros are not necessarily significant.
Example:
(4 sig figs) (2 or 3 or 4 sig figs)

5. 5 Rules
If the number is expressed in scientific notation, all digits in the decimal portion of the number are significant.
Example: x 103
(3 sig figs, only the number before the x 10 count.)

6. Let’s try!!
How many sig figs are in these numbers? (3 sig figs) (5 sig figs) (6 sig figs) (3 sf) (2 sf) (2 sf) (5sf) (5 sf) (2 or 3 sf) (3 or 4 sf)

7. Let’s try!!
1.99 X x 106
(3 sf) (7 sf)

8. Sig Figs with calculations
Addition/Subtraction problems
Imagine a team race where you and your team must finish together. Who dictates the speed of the team?
Of course, the slowest member of the team.
Your answer cannot be MORE precise than the least precise measurement.

9. Addition/Subtraction
Look at the decimal portion (i.e., to the right of the decimal point) of the numbers ONLY. Here is what to do:
Count the number of significant figures in the decimal portion of each number in the problem.
Add/Subtract as usual.
Round the answer to the LEAST number of places in the decimal portion of any number in the problem.

10. Practice Add: 23.1 + 4.77 + 125.39 + 3.581 = Subtract: 22.101 - 0.9307

11. Multiplication/Division
An answer is no more precise that the least precise number used to get the answer.
The LEAST number of significant figures in any number of the problem determines the number of significant figures in the answer.
This means you MUST know how to recognize significant figures in order to use this rule.

12. Practice
2.5 x 3.42 =
3.10 x =
2.33 x x 2.1 =
549 ÷ =