Transcript Chapter 1 Measurements - Department of Chemistry
Chapter 1 Measurements
1.3
Significant Figures in Calculations
Copyright © 2005 by Pearson Education, Inc.
Publishing as Benjamin Cummings
1
Rounding Off Calculated Answers
• • • In calculations, answers must have the same number of significant figures as the measured numbers. often, a calculator answer must be
rounded off
.
rounding rules
are used to obtain the correct number of significant figures.
Copyright © 2005 by Pearson Education, Inc.
Publishing as Benjamin Cummings
2
Rounding Off Calculated Answers
• When the first digit dropped is
4 or less
, the retained numbers remain the same. 45.832 rounded to 3 significant figures drops the digits 32 = 45.8
• When the first digit dropped is
5 or greater
, the last retained digit is increased by 1.
2.4884 rounded to 2 significant figures drops the digits 884 = 2.5 (
increase by 0.1)
3
Adding Significant Zeros
• Sometimes a calculated answer requires more significant digits. Then,
one or more zeros are added.
Calculated
0.2
12
Zeros Added to Answer Give 3 Significant Figures
4 4.
00
1.5
1.5
0
0.2
00
12.
0 4
Learning Check
Adjust the following calculated answers to give answers with three significant figures.
A. 824.75 cm B. 0.112486 g C. 8.2 L
5
Solution
Adjust the following calculated answers to give answers with three significant figures A. 825 cm First digit dropped is greater than 5.
B. 0.112g
First digit dropped is 4.
C. 8.20 L Significant zero is added.
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Calculations with Measured Numbers
In calculations with measured numbers, significant figures or decimal places are counted to determine the number of figures in the final answer.
Copyright © 2005 by Pearson Education, Inc.
Publishing as Benjamin Cummings
7
Multiplication and Division
• • When
multiplying or dividing
use the same number of significant figures as the measurement with the fewest significant figures.
rounding rules to obtain the correct number of significant figures.
Example: 110.5 x 0.048 = 5.304 = 5.3 (rounded)
4 SF 2 SF calculator 2 SF
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Learning Check
Give an answer for the following with the correct number of significant figures.
A. 2.19 x 4.2 1) 9 = B. 4.311 ÷ 0.07 = 1) 61.59
C. 2.54 x 0.0028 = 0.0105 x 0.060 1) 11.3
2) 9.2 2) 62 2) 11 3) 9.198
3) 60 3) 0.041
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Solution
A. 2.19 x 4.2 B. 4.311 ÷ 0.07 C. 2.54 x 0.0028
0.0105 x 0.060 = 2) 9.2 = 3) 60 = 2) 11 On a calculator, enter each number followed by the operation key. 2.54
x
0.0028 0.0105 0.060 = 11.28888889
= 11
(rounded)
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Addition and Subtraction
• • When
adding or subtracting
use the same number of decimal places as the measurement with the fewest decimal places.
rounding rules to adjust the number of digits in the answer.
25.
2
+ 1.
34
26.
54
26.
5
one decimal place two decimal places calculated answer answer with one decimal place
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Learning Check
For each calculation, round the answer to give the correct number of significant figures.
A. 235.05 + 19.6 + 2 = 1) 257 2) 256.7
B. 58.925 - 18.2 = 1) 40.725
2) 40.73
3) 256.65 3) 40.7
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Solution
A. 235.05 +19.6 + 2 256.65 rounds to 257 Answer (1) B. 58.925 -18.2
40.725 round to 40.7
Answer (3)
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