Transcript 6. Significant Figures in Calculations

General, Organic, and
Biological Chemistry
Fourth Edition
Karen Timberlake
Chapter 1
Chemistry and
Measurements
1.6
Significant Figures in
Calculations
© 2013 Pearson Education, Inc.
Lectures
Calculations with Measured
Numbers
The number of significant
figures in measured
numbers are used to limit
the number of significant
figures in the final answer.
Calculators do not provide
the appropriate number of
significant figures.
© 2013 Pearson Education, Inc.
Chapter 1, Section 6
2
Rounding Off
To represent the appropriate number of significant
figures, we use "rules for rounding."
1. If the first digit to be dropped is 4 or less, then it, and
all following digits are simply dropped from the
number.
2. If the first digit to be dropped is 5 or greater, then the
last retained digit of the number is increased by 1.
© 2013 Pearson Education, Inc.
Chapter 1, Section 6
3
Rounding Off
© 2013 Pearson Education, Inc.
Chapter 1, Section 6
4
Multiplication and Division
When multiplying or dividing use
 the same number of significant figures (SF) as the
measurement with the fewest significant figures, and
 the rounding rules to obtain the correct number of
significant figures.
© 2013 Pearson Education, Inc.
Chapter 1, Section 6
5
Learning Check
Give an answer for the following with the correct
number of significant figures.
A. 9
B. 9.2
C. 9.198
A. 61.59
B. 62
C. 60
A. 11.3
B. 11
C. 0.041
3.
© 2013 Pearson Education, Inc.
Chapter 1, Section 6
6
Solution
Give an answer for the following with the correct number
of significant figures.
On a calculator, enter each number followed by the
operation key.
© 2013 Pearson Education, Inc.
Chapter 1, Section 6
7
Adding Significant Zeros
Sometimes we add one or more significant zeros to
the calculator display in order to obtain the correct
number of significant figures needed.
Example:
Suppose the calculator display is 4, and you need
3 significant figures.
4 becomes 4.00
1 SF
© 2013 Pearson Education, Inc.
Chapter 1, Section 6
3 SF
8
Addition and Subtraction
When adding or subtracting, use
 the same number of decimal places as the
measurement with the fewest decimal places and
 the rounding rules to adjust the number of digits in
the answer.
one decimal place
two decimal places
calculated answer
final answer (with one
decimal
place)
© 2013 Pearson Education, Inc.
Chapter 1, Section 6
9
Learning Check
For each calculation, round the answer to give the
correct number of decimal places.
A. 257
B. 256.7
C. 256.65
A. 40.725
B. 40.73
C. 40.7
© 2013 Pearson Education, Inc.
Chapter 1, Section 6
10
Solution
For each calculation, round the answer to give the
correct number of decimal places.
© 2013 Pearson Education, Inc.
Chapter 1, Section 6
11