Significant FiguresSignificant Figures

PurposePurpose

Significant figures are used with any Significant figures are used with any measurementmeasurement

They tell you something about the They tell you something about the accuracy of the tool usedaccuracy of the tool used

Sig figs are the known or certain digits in a Sig figs are the known or certain digits in a measurement plus the estimated digit.measurement plus the estimated digit.

exampleexample

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 Rules All non zero digits are significant because All non zero digits are significant because

they hold a value.they hold a value.Zeros may or may not be significantZeros may or may not be significant

They are significant when they are:They are significant when they are:Between two non zero digitsBetween two non zero digits

10091009 201201

Are trailing with a decimalAre trailing with a decimal 12.0012.00 15.650015.6500

Zeros are not significant when they are:Zeros are not significant when they are:Leading Leading

0.0002560.000256 0.03580.0358

Trailing Trailing withoutwithout a decimal a decimal 100100 150 000150 000

Sig Fig Practice #1Sig 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

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

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) 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

Rules for Significant Figures in Rules for Significant Figures in Mathematical OperationsMathematical Operations

Multiplication and DivisionMultiplication and Division:: # # sig figs in the result equals the sig figs in the result equals the number in the least precise number in the least precise measurement used in the measurement used in the calculation.calculation.

6.38 x 2.0 =6.38 x 2.0 =12.76 12.76 13 (2 sig figs)13 (2 sig figs)

Sig Fig Practice #2Sig Fig Practice #2

3.24 m x 7.0 m

Calculation Calculator says: Answer

22.68 m2 23 m2

100.0 g ÷ 23.7 cm3 4.219409283 g/cm3 4.22 g/cm3

0.02 cm x 2.371 cm 0.04742 cm2 0.05 cm2

710 m ÷ 3.0 s 236.6666667 m/s 240 m/s

1818.2 lb x 3.23 ft 5872.786 lb·ft 5870 lb·ft

1.030 g ÷ 2.87 mL 2.9561 g/mL 2.96 g/mL

Carry out the following calculations:(Answers should be expressed with the correct number of sig figs!)

1. 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 Rules for Significant Figures in Mathematical OperationsMathematical Operations

Addition and SubtractionAddition and Subtraction: The : The number of decimal places in the result number of decimal places in the result equals the number of decimal places in equals the number of decimal places in the least precise measurement.the least precise measurement.

6.8 + 11.934 =6.8 + 11.934 =18.734 18.734 18.7 (3 sig figs)18.7 (3 sig figs)

6.8

+ 11.934

18.734

Sig Fig Practice #3Sig Fig Practice #3

3.24 m + 7.0 m

Calculation Calculator says: Answer

10.24 m 10.2 m

100.0 g - 23.73 g 76.27 g 76.3 g

0.02 cm + 2.371 cm 2.391 cm 2.39 cm

713.1 L - 3.872 L 709.228 L 709.2 L

1818.2 lb + 3.37 lb 1821.57 lb 1821.6 lb

2.030 mL - 1.870 mL 0.16 mL 0.160 mL

Carry out the following calculations:(Answers should be expressed with the correct number of sig figs!)

1. 2.0158 + 16.00

__________ - because

2. 35.453 +

1.0079

__________ - because

3. 207.2 + 70.906

__________ - because

4. 2000 - 46

__________ -

because

5. 5.44 – 2.6103

__________ -

because

6. 216 - .493

__________ -

because