1. Unit 1 lec 3: Significant Figures
What is the difference between the values of 3, 3.0, and 3.00

2. Significant Figures Instruments are only so precise.
The number of digits reported are considered significant figures.
There are rules for determining the number of significant figures.

3. RULE #
1 SIG FIG
2 SIG FIGS
3 SIG FIGS
4 SIG FIGS
5 SIG FIG 1 6 17
183
34.25
12,375 2 3 4

4. Rules for Significant Figures
1. Non-zero numbers are always significant.
Ex  has 3 significant figures.

5. RULE #
1 SIG FIG
2 SIG FIGS
3 SIG FIGS
4 SIG FIGS
5 SIG FIG 1 6 17
183
34.25
12,375 2 10
1500
103
5001
12,305 3 4

6. Rules for Significant Figures
1. Non-zero numbers are always significant.
Ex  has 3 significant figures.
2. Zeros between non-zero numbers are always significant.
Ex  has 3 significant figures.

7. RULE #
1 SIG FIG
2 SIG FIGS
3 SIG FIGS
4 SIG FIGS
5 SIG FIG 1 6 17
183
34.25
12,375 2 10
1500
103
5001
12,305 3 50
50.
125,000
12.00
12.000 4

8. Rules for Significant Figures
1. Non-zero numbers are always significant.
Ex  has 3 significant figures.
2. Zeros between non-zero numbers are always significant.
Ex  has 3 significant figures.
3.Zeros before (to the left of) non-zero numbers are not significant.
Ex  has 3 significant figures

9. RULE #
1 SIG FIG
2 SIG FIGS
3 SIG FIGS
4 SIG FIGS
5 SIG FIG 1 6 17
183
34.25
12,375 2 10
1500
103
5001
12,305 3 50
50.
125,000
12.00
12.000 4
0.0068
502
502.0
502,340,000

10. 4. All Zeros after (to the right of) non-zero numbers are significant IF there is a decimal point in the number.
Ex  5 significant figures (decimal)
Ex. 12,000  2 significant figures (no decimal)
Ex  4 significant figures (decimal)
Ex. 12,000.  5 significant figures (decimal)

11. Let’s try some together….
How many significant digits are in these numbers?
35 g
3.57 m
3.507 km kg
2406 L
.0004 m g g

12. How did you do?
35g 2
3.57m 3
3.507km 4
0.0035kg 2
2406 L 4
.0004m 1
g 5
g 7

13. Rounding Numbers
Often times your calculator will give you more digits than necessary. In these cases you will round. Let try a few.
1. Round to 5 significant figures. =
2. Round to 3 significant figures
= 3.52
3. Round 3.52 to 1 significant figure
= 4
4. Round 3430 to 2 significant figures
= 3400

14. Round all of the numbers to four significant figures
a kg
b g
c cm
d m
e g
f. 136,758 kg
g. 308,659,000 mm
h ml

15. Round all of the numbers to four significant figures
a kg = kg
b g = g
c cm = cm
d m = m
e g = g or x 10-5g
f. 136,758 kg = 136,800 kg or x 105 kg
g. 308,659,000 mm = 308,700,000mm or x 108mm
h ml = ml

16. Calculations with significant figures
1. For addition and subtraction, the answers should be rounded off to the same number of decimal points as the measurement with the fewest decimal places.
Ex = 4.66  4.7
Ex =  56.6
2. For multiplication and division, the answers should be rounded off to the same number of significant figures in the measurement with the fewest significant figures
Ex x 2.0 = 6.02  6.0
Ex. 45 / 9.00 = 5.00  5.0

17. Practice: 4.5 + 2.34 = _____________________
2) 4.5 – 5 = ________________________
3) = _____________________
4) 3.4 x 2.32 = _______________________
5) 7.77 / 2.3 = ______________________
6) / 121 = ______________________

18. 7) 1200 x 23. 4 = ______________________ 8) 120 x 0
7) 1200 x 23.4 = ______________________ 8) 120 x = _____________________ 9) = ___________ 10) (3.4 x 8.90) x ( ) = _________ 11) (2.31 x 103) / (3.1 x 102) = ___________ 12) = __________________