1 Chapter 1 Measurements 1.4 Significant Figures in Calculations Copyright © 2009 by Pearson...
-
Upload
daniella-clark -
Category
Documents
-
view
225 -
download
0
Transcript of 1 Chapter 1 Measurements 1.4 Significant Figures in Calculations Copyright © 2009 by Pearson...
1
Chapter 1 Measurements
1.4Significant Figures in
Calculations
Copyright © 2009 by Pearson Education, Inc.
2
Rounding Off Calculated Answers
In calculations,
• answers must have the same number of significant figures as the measured numbers.
• a calculator answer often must be rounded off.
• rounding rules are used to obtain the correct number of significant figures.
Copyright © 2009 by Pearson Education, Inc.
3
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)
4
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 4.001.5 1.500.2 0.200
12 12.0
5
Learning Check
Round off or add zeros to the following calculated answers to give three significant figures.
A. 824.75 cm
B. 0.112486 g
C. 8.2 L
6
Solution
Adjust the following calculated answers to give answers
with 3 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.
7
Calculations with Measured Numbers
In calculations with measured numbers, significant figures ordecimal places arecounted to determinethe number of figures inthe final answer.
Copyright © 2009 by Pearson Education, Inc.
8
When multiplying or dividing
• the final answer must have the same number of significant figures as the measurement with the fewest significant figures.
• use 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
Multiplication and Division
9
Select the answer 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
10
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 by the operation key.
2.54 x 0.0028 0.0105 0.060 = 11.28888889 = 11
(rounded)
Solution
11
When adding or subtracting
• the final answer must have the same number of decimal places as the measurement with the fewest decimal places.
• use 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 with one decimal place
Addition and Subtraction
12
For each calculation, round off the calculated answer to give a final answer with the correct number of significant figures.
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
13
A. 235.05 +19.6 + 2 256.65 round to 257 Answer (1)
B. 58.925 -18.2
40.725 round to 40.7 Answer (3)
Solution