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
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
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.
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 © 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
4 SF
x
0.048 = 5.304
2 SF
=
calculator
5.3 (rounded)
2 SF
8
Learning Check
Give an answer for the following 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
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)
10
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
11
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
12
Solution
A. 235.05
+19.6
+ 2
256.65 rounds to 257
B.
58.925
-18.2
40.725 round to 40.7
Answer (1)
Answer (3)
13