Chemistry 2015-2016
Significant Figures
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The significant figures are the digits in a number which represent the accuracy of that number. All nonzero digits in a number are significant. But zeros may be just "place holders". The following two
examples show the use of place holders in numbers:
0.085
This number has an accuracy of two significant figures. In this number the "8"
and "5" are measured digits and are therefore significant. The zero is just a place holder that shows
the position of the decimal point; it is not a significant figure.
400
This number has an accuracy of one significant figure. Trailing zeros are often
only place holders. In this number the zeros are there to show that the "4" is in the hundreds column.
Since no decimal point is shown, the zeros have not been measured and are not significant.
Rules for Determining Significant Figures
1. All non-zero digits are significant.
2. Zeros to the left of non-zero digits are NEVER significant.
3. Zeros between non-zero digits are ALWAYS significant.
4. Zeros to the right of non-zero digits are significant ONLY if a decimal point is
shown.
*Notice that the terms left, between and right refer to the placement of the zeros in relationship with
non-zero numbers NOT in relationship with the decimal point.
All non-zero digits are always significant. The following examples illustrate the rules shown above as
they apply to zeros:
rule 2
rule 3
rule 4
number
sig figs
number
sig figs
number
sig figs
007
1
408
3
600
1
.025
2
7.002
4
8,500
2
0.09
1
30.7
3
30.0
3
.0081
2
50,009
5
46,000.
5
Practice Problems
Indicate the number of significant figures and list the rules (by number) that apply to each. You do not
have to list rule 1 every time.
1.
247
6.
0.3
11.
200
2.
2.47
7.
.0074
12.
.04030
3.
4,105
8.
8.00
13.
.00007
4.
.1002
9.
62.000
14.
3,000.
5.
250
10.
.030
15.
1,200
Chemistry 2015-2016
Significant Figure Math
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Date:
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Addition and Subtraction: When doing calculations involving measurements, the answer can only be as
accurate as the least accurate measurement made.
Rule: The answer must be rounded off to the same place value as the least precise measurement
used in the calculation.
Sample Problem
Subtract: 246.58-87.3
Solution
Calculator answer:
159.28
246.58 is significant to the hundredths place. 87.3 is only significant to the tenths place. This means that
our answer must be reported to the tenths place.
Answer:
159.3
Sample Problem
Add:
4,300
+ 928.6
Solution
Calculator answer:
5,228.6
4300 is significant to the 3 (hundreds place). 928.6 is significant to the 6 (tenths place). Our answer can
only be reported as far as the hundreds place
Answer:
5,200
Problems do the addition or subtraction indicated, and round your answer to the correct precision.
1)
9.4
+ 1.47
4)
2)
72.9
- 4.883
5)
3)
3.6
+ 8
6)
300
+ 260
19.868
- 5
4,700
- 520
7)
8)
9)
1.75
105.0
42.02
+ .5483
200.
+ 1.4
18.0
- 6.18
10)
9.3046
.23
400
+ 62.4
11)
.0514
+ .07
12)
37
- 4.29
Rounding: When rounding off numbers, if what you drop off is greater than or equal to five, round up; if
what you drop off is less than five, leave what remains alone.
Example: 150 rounded to the hundreds place is 200, whereas 149 rounded to the hundreds place is 100.
Multiplication and Division: When multiplying of dividing numbers you must count the number of
significant figures in each number and round off the answer to the same number of significant figures as
the least accurate number.
Rule: The answer must be rounded off to the same number of significant figures as the least
accurate measurement used in the calculation.
Sample Problem:
Multiply:
(34.0)*(.0921084)
Solution
Count significant figures:
3
6
Calculator answer:
3.1316856
Our least significant input only has 3 significant digits; therefore our answer should only have 3
significant digits.
Rounded to the correct accuracy:
3.13
Sample Problem:
Divide:
Solution
Count significant figures:
534.168
0.07
6
1
Calculator answer:
76.30971
Our least significant input only has 1 significant digit; therefore our answer should only have 1 significant
digit.
Rounded to the correct accuracy:
80
Problems: Label each number as to how many significant figures it contains. Write down your calculator
answer and then the answer rounded to the correct accuracy.
1.
(16.00) (.617289)
5.
(560) (.0031842)
2.
65.431
.003
6.
(0.050002) (406)
7.
30.5
.050817
8.
128
16
3.
(.030040) (78.00000)
4.
.8000
.20
Chemistry 2015-2016
Significant Figure Math Practice
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Date:
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Directions: Show both your calculator answer and the final answer (rounded correctly).
When Adding or Subtracting
When Multiplying or Dividing
The answer must be rounded off to the same
The answer must be rounded off to the
column (ones, tenths, hundredths, etc.) as the
same number of significant figures as the
least precise measurement used in the
least accurate measurement used in the
calculation.
calculation.
1)
121.6
1.123
+ 31.6
9)
2)
13.421
11.7
10)
342
.007
3)
1511
.00712
11)
(1221) (605)
4)
93.612
34.7113
+ 15.16
12)
13.61
- 1.2
5)
(1359) (2.5)
13)
16.217
- 15.74
6)
7.6
113.2
14)
(256.1) (135.7)
(112) (2)
7)
(2.3) (.00211)
46.1
15)
(7148.571) (.0700)
8)
60.0
- 58.007
16)
1211.21
12.42
+ 1
4.0000
+ 6.00
4