1. SIGNIFICANT figures

2. When do I need to worry about significant figures?
Significant figures are important when you are making a measurement (or when you are using someone else’s measurement)
Significant figures are important when you are doing a math problem and need to report the answer with the correct precision

3. How to determine the number of significant figures when measuring
When measuring, always include one estimated digit
Said Another way - Read the measurement to 1/10 of the smallest division

4. How to determine the number of significant figures when measuring
Ex. #1 – The smallest division on this beaker is 10ml so we will estimate the one’s place and read it as 48ml. We know that we have 40ml for sure and we are estimating the next digit.

5. How to determine the number of significant figures when measuring
Ex. #2 – The smallest division on this graduated cylinder is 1ml so we will estimate to one place after the decimal and read it as 35.4ml . We know the 35ml for sure and we are estimating the next digit.

6. Rules for Determining sig figs
All NON-ZERO numbers are always significant! (1,2,3,4,5,6,7,8,9)
2) ALL zeroes between non-zero numbers are ALWAYS significant.

7. Rules for determining sig figs
3) ALL zeroes which are to the right of the decimal point AND at the end of the number are ALWAYS significant. 4) ALL zeroes which are to the left of a WRITTEN decimal point and are in a number ≥ 10 are ALWAYS significant.

8. EXAMPLES 5
36,453
4.872
400.09
0.0006
9.8000 4 5 1 5

9. EXAMPLES 6
4,000,000
10.0
340 1 3 6 2

10. Significant figures are infinite if you are counting something
Important Exceptions
Significant figures are infinite if you are counting something
Ex. 53 people were present
Significant figures are infinite if you are using a set quantity
Ex. 12 inches in a foot

11. Helpful hint
If you are having trouble, try putting the numbers in scientific notation and then try to figure out the answer. Ex #1) → 3.5 x 10-5 so there are 2 sig. figs. Ex #2) 30,000 → 3 x 104 so there is only 1 sig. fig.

12. Addition & Subtraction
RULES:
Count the number of places after the decimal in each number.
Your answer can only have as many places after the decimal as the number with the fewest places after the decimal.

13. Addition & Subtraction
Examples
= =
36.20 – = =
= =
72.0
13.08 38

14. Multiplication & Division
RULES:
Count the number of significant figures in each number.
Your answer can only have as many significant figures as the number with the fewest significant figures.

15. Multiplication & division
Examples
12.4 x x .04 = =
44.546/12.2 = =
31000 x x = 1,561, = 7
3.65
1,600,000