1. This will not go away this semester, so pay attention!!!
Significant Figures
This will not go away this semester,
so pay attention!!!
Vocabulary:
significant figures
“0-9”, Jasper Johns, 1960

2. Look at this measurement
Every number on the screen is a measured value. Measured values are called significant figures. Which places were measured in this reading? How many significant figures are in the measurement?
99 g

3. Look at this measurement
Answer: 2 Assuming the balance is calibrated correctly, is this the correct mass of the cart?
99 g

4. Looking at this new measurement, was the last measurement of 99 g correct? Was it accurate? How many sig. figs. are in this measurement? What’s the cost? Is this measurement accurate?
98.86 g

5. Looking at this new measurement, was the last measurement of 98
Looking at this new measurement, was the last measurement of g correct? Was it accurate? How many sig. figs. are in this measurement? What’s the cost? Is this measurement accurate? g

6. Look at this measurement
Was every number on this balance’s display measured?
Yes!!!
The zeroes were measured. There were no tenths or hundredths of a gram, and we confirmed it with this balance. The zeroes are significant figures. g

7. Look at this measurement
So how many significant figures are in the measurement? 5 g

8. Significant Figure Rules
All non-zero numbers are significant.
(If you’re reporting a non-zero number, you measured it.)
Example:
mL has how many sig figs? 6

9. Significant Figure Rules
2. All “trapped” zeros are significant.
(A zero between other numbers was measured.)
Example:
8009 miles has how many sig figs? 4

10. Significant Figure Rules
3. If decimal is present, all trailing zeroes are significant.
Example:
81.40 oz has how many sig figs? 4

11. Look at this measurement
Do you think all of these measurements actually ended with zeroes or do you think the scale lacks accuracy in the ones place?

12. Look at this measurement
When finding the mass of a truck that is thousands of pounds, accuracy to the ones place is not important compared to the added cost for the scale. So the ones place is rounded for all of these measurements. Those final zeroes are not significant. (They are important place holders though!)

13. Look at this measurement
So how many significant figures are in measurement 1? 4 How many in measurement 2? How many in measurement 3?

14. Significant Figure Rules
4. If decimal is not present, all trailing zeroes are NOT significant.
Example:
560 lb has how many sig figs? 2
13000 lb has how many sig figs? 3

15. Significant Figure Rules
If I told you my weight is lb, are the zeroes in front significant?
No. They were not measured. I do not have any thousands of pounds or ten-thousands of pounds to measure!
The same is true with very small measurements like lb. The zeroes in front were not measured because the object did not have any tenths or hundredths of pounds to measure. The leading zeroes are NOT sig.

16. Significant Figure Rules
5. All leading zeroes are NOT significant.
Example:
L has how many sig figs? 3
mg has how many sig figs? 4

17. Significant Figure Rules
6. Numbers that are counted and not measured have infinite significant figures.
Example:
12 books
10 fingers
101 Dalmatians

18. Significant Figure Rules
7. All digits in scientific notation are significant.
Example:
3.5 x 103 m has how many sig figs? 2
4.270 x 10-4 kg has how many sig figs? 4

19. Practice
482
4092
0.0300
12.00
890,000
40920
3400.
3.1x10-2
240000 58
1000
300005
3.00x104
240000
2,300

20. Now for the application

21. Mult. and Div. Rules
Your answer should only have the number of sig fig as the measurement in the problem with the least sig fig.

22. Example
34.29 x 0.93 = 32

23. Example
/ =

24. Example
36.2 x 120 =
4344
4300

25. Add. and Subt. Rules
Your answer should be rounded to the same place as the number with the least precise place.

26. Example =
1076.5

27. Example
175

28. Example =
8215.4
8200