Significant Figures

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

 Zeros are not significant when they are:  Leading  0.000256

 0.0358

 Trailing

without

a decimal  100  150 000

Sig Fig Practice #1

How many significant figures in each of the following?

1.0070 m  17.10 kg  100 890 L  3.29 x 10 3 s  0.0054 cm  3 200 000  5 sig figs 4 sig figs 5 sig figs 3 sig figs 2 sig figs 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.

28.6

3 440.00

___ sig figs ___ sig figs 910 ___ sig figs 4.06 x 10 3 ___ sig figs 0.006 700 ___ sig figs 804.05

___ sig figs 0.014 403 ___ sig figs 1.44 x 10 -2 ___ sig figs 400 30 000.

1002 ___ sig figs ___ sig figs ___ sig figs

Round each of the following measurements to the indicated number of significant figures.

__________ 1) 2.68

to 2 significant figures __________ 2) 47.374

__________ 3) 4.165

to 3 significant figures to 3 significant figures __________ 4) 24 __________ 5) 24 __________ 6) 0.048

__________ 7) 0.06350 to 1 significant figure to 3 significant figures to 2 significant figures to 3 significant figures __________ 8) 0.00045 __________ 9) 2007 __________ 10) 36.20499 __________ 11) 0.023600

to 1 significant figure to 3 significant figures to 4 significant figures to 4 significant figures

1.

2.

3.

4.

5.

6.

7.

8.

9.

2.7

47.4

4.17

20 24.0

0.048

0.0635

0.0005

2010 10.

36.20

11.

0.02360

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)

Sig Fig Practice #2

Calculation

3.24 m x 7.0 m 100.0 g ÷ 23.7 cm 3 0.02 cm x 2.371 cm 710 m ÷ 3.0 s 1818.2 lb x 3.23 ft 1.030 g ÷ 2.87 mL

Calculator says:

22.68 m 2 4.219409283 g/cm 0.04742 cm 2 236.6666667 m/s 5872.786 lb·ft 2.9561 g/mL 3

Answer

23 m 2 4.22 g/cm 3 0.05 cm 2 240 m/s 5870 lb·ft 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 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

Sig Fig Practice #3

Calculation

3.24 m + 7.0 m 100.0 g - 23.73 g 0.02 cm + 2.371 cm 713.1 L - 3.872 L 1818.2 lb + 3.37 lb 2.030 mL - 1.870 mL

Calculator says:

10.24 m 76.27 g 2.391 cm 709.228 L 1821.57 lb 0.16 mL

Answer

10.2 m 76.3 g 2.39 cm 709.2 L 1821.6 lb 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