1. Significant Figures

2. Why do we need to know significant figures?
We as scientists need to measure things as we perform experiments.
Instruments have different degrees of precision
We measure to the last known calibration, and estimate the unknown.

3. The Rules

5. Significant Figures – The Rules
1. Nonzero numbers 1 – 9 are always significant.
Examples:
1 meter sig fig
92 liters sig figs
34578 grams sig figs

6. Significant Figures – The Rules
2. Imbedded zeros (zeros between nonzero numbers) are always significant.
Examples:
202 cm 3 sig figs
10509 mL 5 sig figs
2039 kg 4 sig figs
90009 g 5 sig figs

7. Significant Figures – The Rules
3. Leading zeros are never significant.
4. Trailing zeros after a nonzero number after the decimal are significant.
Examples:
g 3 sig figs
mm 4 sig figs
L 3 sig figs

8. Significant Figures – The Rules
5. Trailing zeros before the decimal are significant only if the decimal point is specified.
Examples:
100. dg 3 sig figs
100 dg 1 sig fig
8900 km 2 sig figs
8900. km 4 sig figs

9. Exact Numbers
An exact number is a number that cannot be changed. (Cannot be halved or split up)
Ex. 2 atoms, 1 proton, a hundred dollar bill
We include most conversion factors as exact numbers
Ex. 1m = 100 cm
When you work with exact numbers, you consider them to have infinite sig figs.
(You don’t have to worry about them!)

10. 0.00770800 RECAP #1 Leading Zeros Imbedded Zero after the decimal
Nonzero numbers Trailing Zeros
after the decimal

11. 6 significant figures

12. 22060 RECAP #2 (none) Nonzero numbers Trailing zero with no decimal
Leading Zeros Imbedded Zero
(none)
22060
Nonzero numbers Trailing zero with no decimal

13. 4 significant figures

14. Lets Practice!

15. 56 meters
2 sig figs
Rule 1

16. 20 grams
1 sig fig Rule 1, 5

17. 303.0 mL
4 sig figs Rule 1, 2, 4

18. 200 kilograms
1 sig fig Rule 1, 5

19. 207 kilometers
3 sig figs Rule 1,2

20. grams
4 sig figs Rule 1,3,4

21. m
5 sig figs Rule 1,2,3,4

22. km
3 sig figs Rule 1,2,5

23. 1.10 x 102 hm
3 sig figs Rule 1, 4

24. 2.2 x 1034 atoms
infinite sig figs

25. Rounding Numbers
If you have to round and the number you are looking to round is less than 5, don’t round.
Example:
214
round to 2 s.f.
Answer = 210

26. Rounding Numbers
If you have to round and the number you are looking to round is 5 or greater, round up.
Example:
215
round to 2 s.f.
Answer = 220

27. Adding and subtracting with significant figures.
When adding or subtracting significant figures, you round your answer to the least number of places after the decimal that are contained in your problem.

28. YOU ARE LOOKING AT PLACES AFTER THE DECIMAL NOT SIGNIFICANT FIGURES!

29. Example:
= 6.0
You look for the least number of PLACES after the decimal.
2.00 = 2 places after the decimal
4.0 = 1 place after the decimal
Your answer can only have one place after the decimal.

30. 2.0 + 4 = 6 Example: 2.0 = 1 place after the decimal
4 = no places after the decimal
Your answer can not have any places after the decimal.

31. Example:
– =
=0.055
= 5 places after the decimal
0.001 = 3 places after the decimal
Your answer can only have 3 places after the decimal.

32. Let’s Practice
17.0 – =
Answer
16.5

33. =
Answer 56

34. 100.0 – = 28.48
Answer 28.5

35. =
Answer 20

36. Multiplying and Dividing with Significant Figures
When multiplying or dividing with significant figures, your answer must be rounded to the least number of significant figures in the problem.

37. YOU ARE LOOKING AT SIGNIFICANT FIGURES NOT PLACES AFTER THE DECIMAL!

38. Example
20.0 x = 284.4
Answer
284

39. 430 x = 1.29
Answer 1

40. 2020 x =
Answer
1.60 x 106

41. 50.0 / = 2500
Answer
2500

42. 50.0 / = 2500
Answer
2.50 x 103