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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.

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

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

- Between two non zero digits

- They are significant when they are:

- Zeros are not significant when they are:
- Leading
- 0.000256
- 0.0358

- Leading
- Trailing without a decimal
- 100
- 150 000

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

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 aren’t significant.

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) 24to 1 significant figure

__________ 5) 24to 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) 0.023600to 4 significant figures

- 2.7 number of significant figures.
- 47.4
- 4.17
- 20
- 24.0
- 0.048
- 0.0635
- 0.0005
- 2010
- 36.20
- 0.02360

Rules for Significant Figures in Mathematical Operations number of significant figures.

- 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)

Sig Fig Practice #2 number of significant figures.

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 lb·ft

1818.2 lb x 3.23 ft

5872.786 lb·ft

2.9561 g/mL

2.96 g/mL

1.030 g ÷ 2.87 mL

Carry out the following calculations: number of significant figures.(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

Rules for Significant Figures in Mathematical Operations number of significant figures.

- 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

Sig Fig Practice #3 number of significant figures.

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

Carry out the following calculations: number of significant figures.(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