1. Significant Figures
The Four Rules

2. Rule #1: All non-zero numbers are always…
SIGNIFICANT!!! 4 3 6 9 2 7 8 1 5

3. So, the only number to worry about is…

4. Rule # 2
All trapped zeros are always significant Example: significant Figures Significant Figurs

5. The Other Zero Rules Rule #3:
All final zeros to the ______ of a decimal point are significant.
right
Rule #4:
Zeros that act as ____________ are NOT significant.
Also known as “LEADING” zeros
placeholders

6. Significant? .0

7. Another note: if a number is written in scientific notation, all numbers before the x 10 are significant, all numbers after are not significant.

8. Is It Significant?

9. 16407.100 0.00010080 904008000 Significant Non-Significant 8 sig figs

10. Let’s look at some examples
a L
b L
c x 104 kg
d kg
4 significant figures
7 significant figures
5 significant figures
3 significant figures

11. Let’s look at some examples
a s
b mL
c x 10-8 g
d mL
5 significant figures
3 significant figures
5 significant figures
2 significant figures

12. So, why are significant figures important?
Significant figures and math

13. Addition and Subtraction
When adding or subtracting—the answer has the least number of decimal places
Hint: Before adding and subtracting, line up all the numbers so the decimal points align.
187.6
961.95
18.95
189.9 19

14. Multiplication and Division
When multiplying or dividing—the product has the least number of significant figures
21.6 x
(3 sig figs)
7216 ÷
(4 sig figs)
(2 sig figs)
(2 sig figs)
1.4472
(2 sig figs)
(2 sig figs)
1.4
210000
Or 2.1 x 105

15. Now, try some of these on your own

16. Addition a) 43.2 cm 51.0 cm + 48.7 cm b) 258.3 kg 257.1 1 kg + 253 kg
c) mg mg mg kg mg
142.9 cm
768 kg mg

17. Multiplication a) 24 m x 3.26 m = 78.24 m = 78 m b) 120 m x 0.10 m
c) 1.23 m x 2.0 m
= 2.46 m
= 2.5 m
d) 53.0 m x 1.53 m
= m
= 81.1 m

18. Why do we have them?
When we measure things, we want to measure to the place we are sure of and guess one more space.

19. So, they show the uncertainty in our measurements

20. Since the marks on this ruler are subdivided as they are, our answer for the length of this nail has 3 significant figures.

21. However, we only have significant figures when we are measuring something. Counting will give you an exact number.