1. Significant Figures
© R. A. Hill

2. significant figures (def) – All those digits in a measurement known to be
accurate plus one more which is an estimate.

3. significant figures (def) – All those digits in a measurement known to be
accurate plus one more which is an estimate.
5.4 m m 1 2 3 4 5 6 7

4. significant figures (def) – All those digits in a measurement known to be
accurate plus one more which is an estimate.
5.4 m m 1 2 3 4 5 6 7

5. significant figures (def) – All those digits in a measurement known to be
accurate plus one more which is an estimate.
5.4 m m 1 2 3 4 5 6 7

6. significant figures (def) – All those digits in a measurement known to be
accurate plus one more which is an estimate.
5.37 m m 5 7 6

7. significant figures (def) – All those digits in a measurement known to be
accurate plus one more which is an estimate.
5.37 m m 5 7 6

8. significant figures (def) – All those digits in a measurement known to be
accurate plus one more which is an estimate.
5.37 m m 5 7 6

9. significant figures (def) – All those digits in a measurement known to be
accurate plus one more which is an estimate. m
0.4
0.1
0.2
0.3 5 m

10. significant figures (def) – All those digits in a measurement known to be
accurate plus one more which is an estimate. m
0.4
0.1
0.2
0.3 5 m

11. significant figures (def) – All those digits in a measurement known to be
accurate plus one more which is an estimate. m
0.4
0.1
0.2
0.3 5 m
In every measurement there are accurately known, estimated and unknown digits.

12. The problem…

13. 5 . 0 4 3 + 1 . 2 0 0 The problem… Assume there are zeros …
Assume there are zeros …
But that is a guess,
if measured with a device of greater accuracy it could be anything…

14. 5 . 0 4 3 + 1 . 2 0 0 The problem… There are then 3 types of digits:
guesses

15. 5 . 0 4 3 + 1 . 2 0 0 The problem… There are then 3 types of digits:
guesses
estimates
accurately known

16. 5 . 0 4 3 + 1 . 2 0 0 6 . 2 4 3 The problem… There are then
3 types of digits:
guesses
estimates
accurately known
Classify the digits in the answer.

17. 5 . 0 4 3 + 1 . 2 0 0 6 . 2 4 3 The problem… There are then
3 types of digits:
guesses
estimates
accurately known
Classify the digits in the answer.

18. 5 . 0 4 3 + 1 . 2 0 0 6 . 2 4 3 The problem… There are then
3 types of digits:
guesses
estimates
accurately known
Classify the digits in the answer.

19. 5 . 0 4 3 + 1 . 2 0 0 6 . 2 4 3 The problem… There are then
3 types of digits:
guesses
estimates
accurately known
Classify the digits in the answer.
Guesses are not significant figures.
So the answer is…

20. 5 . 0 4 3 + 1 . 2 0 0 6 . 2 The problem… There are then
3 types of digits:
guesses
estimates
accurately known
6 . 2
Classify the digits in the answer.
Guesses are not significant figures.
So the answer is…
Classify the digits in the answer.
Guesses are not significant figures.

21. 5 . 0 4 3 + 1 . 2 0 0 6 . 2 The problem… There are then
3 types of digits:
guesses
estimates
accurately known
6 . 2
To get rid of guesses in answers more quickly & simply:
1st we must be able to identify significant digits (accurate and estimated digits in measurements)
2nd we learn how to round away guesses in the answers from all operations.

22. Rules for Identifying the # of S.F. in a Measurement
If a measurement is made correctly, all the nonzero digits are significant figures.
Zeros are significant or not depending on their position within the measurement.

23. Markings every: 1000 ml 100 ml 10 ml 1 ml 400 ml 380 ml 380 ml
Same liquid sample
in 4 different graduated cylinders.
400 ml
380 ml
380 ml
380.4 ml
Zeros may be significant (measured accurately or estimated) or may not be significant (not measured).

24. Zeros in the front portion of a # are never significant. 0.32 2 S.F.
Zeros in the front portion of a # are never significant.
  S.F.
S.F.

25. Zeros between significant digits in a # are always significant.
Zeros between significant digits in a # are always significant.
S.F.
S.F.

26. Zeros at the end of a # and to the right of the decimal are
Zeros at the end of a # and to the right of the decimal are
always significant.
S.F.
S.F.

27. Zeros at the end of a # and to the left of the decimal may
Zeros at the end of a # and to the left of the decimal may
or may not be significant.
1 700
2 to 4 S.F. ?

28. Zeros at the end of a # and to the left of the decimal may
Zeros at the end of a # and to the left of the decimal may
or may not be significant.
1 700
2 to 4 S.F. ?

29. Zeros at the end of a # and to the left of the decimal may
Zeros at the end of a # and to the left of the decimal may
or may not be significant.
1 700
2 to 4 S.F. ?

30. Zeros at the end of a # and to the left of the decimal may
Zeros at the end of a # and to the left of the decimal may
or may not be significant.
1 700
2 to 4 S.F. ?

31. Zeros at the end of a # and to the left of the decimal may
Zeros at the end of a # and to the left of the decimal may
or may not be significant.
1 700
2 to 4 S.F. ?
3 to 7 S.F. ?

32. Zeros at the end of a # and to the left of the decimal may
Zeros at the end of a # and to the left of the decimal may
or may not be significant.
1 700
2 to 4 S.F. ?
3 to 7 S.F. ?

33. Zeros at the end of a # and to the left of the decimal may
Zeros at the end of a # and to the left of the decimal may
or may not be significant.
1 700
2 to 4 S.F. ?
3 to 7 S.F. ?

34. Zeros at the end of a # and to the left of the decimal may
Zeros at the end of a # and to the left of the decimal may
or may not be significant.
1 700
2 to 4 S.F. ?
3 to 7 S.F. ?

35. Zeros at the end of a # and to the left of the decimal may
Zeros at the end of a # and to the left of the decimal may
or may not be significant.
1 700
2 to 4 S.F. ?
3 to 7 S.F. ?

36. Zeros at the end of a # and to the left of the decimal may
Zeros at the end of a # and to the left of the decimal may
or may not be significant.
1 700
2 to 4 S.F. ?
3 to 7 S.F. ?

37. How many significant figures are in the following measurements?
(1)
(2)
(3) 302
(4)
(5)
(6)
(7)
(8)
(9)
(10)
(11)
(12) 300
(13) 1700
(14)
(15)
(16) 15