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
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