Transcript Chapter 1 Measurements

Chapter 1
Measurements
1.4
Significant Figures in
Calculations
Copyright © 2009 by Pearson Education, Inc.
1
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.
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
Answer
4
1.5
0.2
12
Zeros Added to
Give 3 Significant Figures
4.00
1.50
0.200
12.0
4
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
5
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.
6
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 © 2009 by Pearson Education, Inc.
7
Multiplication and Division
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
4 SF
x
0.048 = 5.304
2 SF
=
calculator
5.3 (rounded)
2 SF
8
Learning Check
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
9
Solution
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)
10
Addition and Subtraction
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
+ 1.34
26.54
26.5
one decimal place
two decimal places
calculated answer
final answer with one decimal place
11
Learning Check
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
B.
58.925 - 18.2 =
1) 40.725
2) 40.73
3) 256.65
3) 40.7
12
Solution
A. 235.05
+19.6
+ 2
256.65 round to 257
B.
58.925
-18.2
40.725 round to 40.7
Answer (1)
Answer (3)
13