Download 5. Measured Numbers and Significant Figures

General, Organic, and
Biological Chemistry
Fourth Edition
Karen Timberlake
Chapter 1
Chemistry and
Measurements
1.5
Measured Numbers and
Significant Figures
© 2013 Pearson Education, Inc.
Lectures
Representing Measured Numbers
Measured numbers are numbers obtained by using
measuring devices, such as
 a scale or analytical balance,
 a graduated cylinder,
 a clock or stopwatch, or
 a ruler
© 2013 Pearson Education, Inc.
Chapter 1, Section 5
2
Representing Measured Numbers
On a metric ruler with lines marking divisions of 0.1
cm, write the length to 0.1 cm and estimate the value
of the final number to 0.01 cm by visual inspection.
© 2013 Pearson Education, Inc.
Chapter 1, Section 5
3
Rules for Significant Figures
In a measured number, the significant figures (SFs)
are all digits including the estimated number.
A number is a significant figure if it is
 a nonzero number.
(234 g, 3 SF)
 a zero between nonzero numbers.
(50071 g, 5 SF)
 a zero at the end of a decimal number.
(50.00 m, 4 SF)
 the coefficient of a number is written in
scientific notation.
(2.0 x 103 m, 2 SF)
© 2013 Pearson Education, Inc.
Chapter 1, Section 5
4
Scientific Notation and Significant
Zeros
When one or more zeros in a large number are
significant, they are shown more clearly by writing the
number in scientific notation.
5,000. kg
5.000 x 103 kg
If zeros are not significant, we use only the nonzero
numbers in the coefficient.
5,000 kg
© 2013 Pearson Education, Inc.
5 x 103 kg
Chapter 1, Section 5
5
Exact Numbers
Exact numbers are
 those numbers obtained by counting items.
 those numbers in a definition comparing two units
in the same measuring system.
 not measured and do not affect the number of
significant figures in a calculated answer.
© 2013 Pearson Education, Inc.
Chapter 1, Section 5
6
Learning Check
Identify the following as exact or measured numbers.
1. 824.75 cm
2. 23 students in the class
3. 1 m = 1000 cm
© 2013 Pearson Education, Inc.
Chapter 1, Section 5
7
Solution
Identify the following as exact or measured numbers:
1. 824.75 cm
measured number
2. 23 students in the class
exact number
3. 1 m = 1000 cm
exact number
© 2013 Pearson Education, Inc.
Chapter 1, Section 5
8
Learning Check
How many significant figures are in the following numbers?
1. 8250 cm
2. 0.012 g
3. 8.20 L
4. 3.040 x 10−2 m
© 2013 Pearson Education, Inc.
Chapter 1, Section 5
9
Solution
How many significant figures are in the following numbers?
1. 8250 cm
3 significant figures
2. 0.012 g
2 significant figures
3. 8.20 L
3 significant figures
4. 3.040 x 10−2 m
4 significant figures
© 2013 Pearson Education, Inc.
Chapter 1, Section 5
10