1. Significant Figures
L. Bernard, 2015

2. What do I mean if I say that a number is significant?
Do Now!!!!
What do I mean if I say that a number is significant?
L. Bernard, 2015

3. Introduction to sig figs
L. Bernard, 2015

4. All measurements have some degree of uncertainty
Due to the natural faultiness of lab instruments and human error
You are only as “certain” as your instruments!
L. Bernard, 2015

5. What are significant figures?
Numbers that represent how well you actually measured or reported data
Tell the degree of uncertainty associated with data
L. Bernard, 2015

6. Rules for determining significant digits within a number
ALL non-zero digits are ALWAYS significant!
ALL zero’s in-between non-zero digits are ALWAYS significant
Zero’s at the end of a number WITHOUT at decimal point ARE NOT significant
Zero’s at the end of a number WITH a decimal point ARE significant
Zero’s that are before a non-zero digit ARE NOT significant
L. Bernard, 2015

7. Atlantic-Pacific Rule!
If the decimal point is PRESENT, start on the Pacific side (the left) and count over find the first non-zero digit. All numbers after are significant!
If the decimal point is ABSENT, start on the Atlantic side (the right) and count over until you find the first non-zero digit. All numbers after are significant!
L. Bernard, 2015

8. Helpful Tricks Place a decimal point at the end of the number Ex: 100.
The decimal means these zeros are significant and we have 3 significant digits
Re-write the number in scientific notation
Ex: 4,000,000
If we wanted to write this number with 2 significant digits, we could write it as 4.0 x 106
L. Bernard, 2015

9. Practice: How many sig figs in the following numbers?
3,007
56,040
0.15
4.000
810.
x 1036
8.3 x 107
7.13
2,000,000,000,000 05
L. Bernard, 2015

10. Operations with sig figs
L. Bernard, 2015

11. Math operations with sig figs
When doing math with significant figures, the answer reflects the uncertainty of the LEAST PRECISE number
You cannot have an answer more precise than the least precise number
L. Bernard, 2015

12. Addition and subtraction
Look at the number of decimal places within the numbers of the problem
The answer should be rounded to the LEAST amount of decimal places =
We need two decimal places, so the answer will be 15.96
L. Bernard, 2015

13. Multiplication and Division
Look at the number of significant figures within the numbers of the problem
12 x 300
The answer should be rounded to the LEAST amount of significant figures
12 x 300 = 3600
The answer can only have one sig fig so my rounded answer will be 4000.
L. Bernard, 2015

14. Do Now!!!!
Why wouldn’t an exact number (something like pi or how many eggs in a dozen) affect the number of sig figs at the end of math problem?
L. Bernard, 2015

15. Exact numbers
Some numbers will remain EXACT when doing math operations
Constants
We consider exact numbers to have an “infinite” number of significant figures
Exact numbers DO NOT contribute to the significant figures of the problem!
L. Bernard, 2015