1. Significant figures

2. Significant figures:
Are the numbers in a measurement that include all of the digits that are known, plus the last digit that is estimated.

3. Calculating can change the # of significant digits
Calculating can change the # of significant digits. The following rules will help you determine how many significant figures a reported measurement has.

4. Rule #1
Every non zero number is assumed to be significant.

5. Examples:
98 = 2 significant digits
= 6 significant digits
.555 = 3 significant digits

6. Rule #2
Zero’s appearing between non zero numbers are significant.

7. 101 = 3 significant digits 100000.00001 = 11 significant digits
Examples:
101 = 3 significant digits
= 11 significant digits
.6509 = 4 significant digits

8. Rule 3
The left most zeros appearing in front of significant digits are not significant.
They are considered place holders.

9. Examples: 000.0055 = 2 significant digits

10. Rule 4
Zeros at the end of a number that are on the right of any non zero number are always significant, when a decimal is present.

11. Examples: 0.055500 = 5 significant digits

12. Rule 5 (an exception to rule 4)
Numbers that are to the right of a non zero number where there is no decimal present are not significant. Unless it is stated that the measurement is known precisely.

13. Examples: 5000 = 1 significant digits 550100 = 4 significant digits
(The zero between the 1 and the decimal is significant because it is between the significant zero’s after the decimal.)

14. Rule 6 You have an unlimited number of significant figs if you :
Come up with the number by counting every thing.
Are getting the number by converting within a system of measurement.

15. Examples:
I counted = 5 significant digits
There are 1000 meter in 1 Km = 4 significant digits
There are 3600 seconds in 1 hour = 4 significant digits

16. Calculating Significant Digits
When multiplying or dividing measurements, the final answer can not have more sig digs than the measurement with the smallest # of significant digs.

17. Example:
50.0 grams x 3.0 = 150
grams \ 8.3 = 6.0

18. Calculating Adding and Subtracting
When adding and subtracting, the answer must have the same number of decimal places as the number with the least number of decimal places.

19. Example:
50 grams grams =
54 grams
grams grams = 41.7 grams