Significant Figures

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Significant Figures
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Purpose

• Significant figures are used with any measurement
• They tell you something about the accuracy of the
  tool used
• Sig figs are the known or certain digits in a
  measurement plus the estimated digit.

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example
In the above measurement you are certain it is 64
since the object is between the marked 64 and 65.
you then guess the next digit So for this
measurement I would say it is 64.3
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Rules

• All non zero digits are significant because they
  hold a value.
• Zeros may or may not be significant
• They are significant when they are
• Between two non zero digits
• 1009
• 201
• Are trailing with a decimal
• 12.00
• 15.6500

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• Zeros are not significant when they are
• Leading
• 0.000256
• 0.0358
• Trailing without a decimal
• 100
• 150 000

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Sig Fig Practice 1
How many significant figures in each of the
following?
1.0070 m ?
5 sig figs
17.10 kg ?
4 sig figs
100 890 L ?
5 sig figs
3.29 x 103 s ?
3 sig figs
0.0054 cm ?
2 sig figs
3 200 000 ?
2 sig figs
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Determine the number of significant figures in
each measurement using the rules just talked
about. Carefully circle the significant figures
in each example. State the number of significant
figures, and list the rule/s that helped you
determine which zeroes are and arent
significant.
28.6 ___ sig figs
3 440.00 ___ sig figs
910 ___ sig figs
4.06 x 103 ___ sig figs
0.006 700 ___ sig figs
804.05 ___ sig figs
0.014 403 ___ sig figs
1.44 x 10-2 ___ sig figs
400 ___ sig figs
30 000. ___ sig figs
1002 ___ sig figs
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Round each of the following measurements to the
indicated number of significant
figures. __________ 1) 2.68 to 2 significant
figures __________ 2) 47.374 to 3
significant figures __________ 3) 4.165 to 3
significant figures __________ 4) 24 to 1
significant figure __________ 5) 24 to 3
significant figures __________ 6) 0.048 to 2
significant figures __________ 7) 0.06350 to 3
significant figures __________ 8) 0.00045 to 1
significant figure __________ 9) 2007 to 3
significant figures __________ 10) 36.20499
to 4 significant figures __________ 11)
0.023600 to 4 significant figures
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1. 2.7
2. 47.4
3. 4.17
4. 20
5. 24.0
6. 0.048
7. 0.0635
8. 0.0005
9. 2010
10. 36.20
11. 0.02360

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Rules for Significant Figures in Mathematical
Operations

• Multiplication and Division sig figs in the
  result equals the number in the least precise
  measurement used in the calculation.
• 6.38 x 2.0
• 12.76 ? 13 (2 sig figs)

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Sig Fig Practice 2
Calculation
Calculator says
Answer
22.68 m2
3.24 m x 7.0 m
23 m2
100.0 g 23.7 cm3
4.22 g/cm3
4.219409283 g/cm3
0.02 cm x 2.371 cm
0.05 cm2
0.04742 cm2
710 m 3.0 s
236.6666667 m/s
240 m/s
5870 lbft
1818.2 lb x 3.23 ft
5872.786 lbft
2.9561 g/mL
2.96 g/mL
1.030 g 2.87 mL
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Carry out the following calculations(Answers
should be expressed with the correct number of
sig figs!)

• 13.62 x 1.7
• __________ - because
• 2. 175.67 x 3.950
• __________ - because
• 3. 2.4 x 15.8
• __________ - because

4. 87.35 / 0.016 __________ - because 5.
2.67 / 0.890 __________ - because 6. 46.37 /
20 __________ - because
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Rules for Significant Figures in Mathematical
Operations

• Addition and Subtraction The number of decimal
  places in the result equals the number of decimal
  places in the least precise measurement.
• 6.8 11.934
• 18.734 ? 18.7 (3 sig figs)

6.8 11.934 18.734
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Sig Fig Practice 3
Calculation
Calculator says
Answer
10.24 m
3.24 m 7.0 m
10.2 m
100.0 g - 23.73 g
76.3 g
76.27 g
0.02 cm 2.371 cm
2.39 cm
2.391 cm
713.1 L - 3.872 L
709.228 L
709.2 L
1821.6 lb
1818.2 lb 3.37 lb
1821.57 lb
0.160 mL
0.16 mL
2.030 mL - 1.870 mL
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Carry out the following calculations(Answers
should be expressed with the correct number of
sig figs!)
4. 2000 - 46 __________ - because 5. 5.44
2.6103 __________ - because 6. 216 -
.493 __________ - because
1. 2.0158 16.00 __________ - because 2.
35.453 1.0079 __________ - because 3. 207.2
70.906 __________ - because
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