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


1009
201
 Are


two non zero digits
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 
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.
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
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
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
36.20
11. 0.02360
10.
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
Calculator says:
Answer
3.24 m x 7.0 m
22.68 m2
100.0 g ÷ 23.7 cm3
4.219409283 g/cm3 4.22 g/cm3
23 m2
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
4.
87.35 / 0.016
__________ - because
2. 175.67 x 3.950
5.
__________ - because
__________ - because
3. 2.4 x 15.8
6. 46.37 / 20
__________ - because
__________ - because
2.67 / 0.890
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
Calculator says:
Answer
3.24 m + 7.0 m
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
4.
2000 - 46
__________ - because
__________ - because
2.
5.
35.453 + 1.0079
5.44 – 2.6103
__________ - because
__________ - because
3.
6.
207.2 + 70.906
__________ - because
216 - .493
__________ - because