1 chapter 2 measurements 2.4 significant figures in calculations basic chemistry copyright © 2011...
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1
Chapter 2 Measurements
2.4Significant Figures in
Calculations
Basic Chemistry Copyright © 2011 Pearson Education, Inc.
2
Rounding Off Answers
In calculations
• answers must have the same number of significant figures as the measured numbers
• calculated answers are usually rounded off
• rounding rules are used to obtain the correct number of significant figures
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Rounding Off Calculated Answers
• When the first digit dropped is 4 or less, the retained numbers remain the same.
to round off 45.832 to 3 significant figures
drop the digits 32 = 45.8
• When the first digit dropped is 5 or greater, the last retained digit is increased by 1.
to round off 2.4884 to 2 significant figures
drop the digits 884 = 2.5 (increase by 0.1)
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Adding Significant Zeros
• Sometimes a calculated answer requires more significant digits. Then one or more zeros are added.
Calculated Zeros Added to Answer Give 3 Significant
Figures 4 4.00 1.5 1.50 0.2 0.200
12 12.0
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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
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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 added
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Calculations with Measured Numbers
In calculations with measured numbers, significant figures or decimal places are used to determine the correct number of figures in the final answer.
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When multiplying or dividing, use
• the same number of significant figures (SFs) as in 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 SFs 2 SFs calculator 2 SFs
Multiplication and Division
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Give an answer for each with the correct
number of significant figures.
A. 2.19 x 4.2 =
1) 9 2) 9.2 3) 9.198
B. 4.311 ÷ 0.07 = 1) 61.59 2) 62 3) 60
C. 2.54 x 0.0028 =
0.0105 x 0.060
1) 11.3 2) 11 3) 0.041
Learning Check
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A. 2.19 x 4.2 = 2) 9.2
B. 4.311 ÷ 0.07 = 3) 60
C. 2.54 x 0.0028 = 2) 11
0.0105 x 0.060
On a calculator, enter each number followed bythe operation key.
2.54 x 0.0028 0.0105 0.060 = 11.28888889
= 11 (rounded off)
Solution
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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 one decimal place
+ 1.34 two decimal places
26.54 calculated answer
26.5 final answer (one decimal place)
Addition and Subtraction
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For each calculation, round the answer to givethe correct number of digits.
A. 235.05 + 19.6 + 2 = 1) 257 2) 256.7 3) 256.65
B. 58.925 - 18.2 =1) 40.725 2) 40.73 3) 40.7
Learning Check
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A. 235.05 hundredths place (2 decimal places)
+19.6 tenths place (1 decimal place) + 2 ones place 256.65 rounds to 257 answer (1)
B. 58.925 thousandths place (3 decimal places) -18.2 tenths place (1 decimal place)
40.725 round to 40.7 answer (3)
Solution
Basic Chemistry Copyright © 2011 Pearson Education, Inc.