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Chapter
7
Decimals: Rational
Numbers and
Percent
Copyright © 2013, 2010, and 2007, Pearson Education, Inc.
NCTM Standard: Decimals and
Real Numbers
Students in grades 6−8 should
 work flexibly with fractions, decimals, and percents to
solve problems;
 compare and order fractions, decimals, and percents
efficiently and find their approximate locations on a
number line;
 develop an understanding of large numbers and
recognize and appropriately use exponential,
scientific, and calculator notation;
 understand the meaning and effects of arithmetic
operations with fractions, decimals, and integers.
(p. 214)
Copyright © 2013, 2010, and 2007, Pearson Education, Inc.
7-1 Introduction to Decimals
Representations of Decimals
Ordering Terminating Decimals
Copyright © 2013, 2010, and 2007, Pearson Education, Inc.
Decimals
The word decimal comes from the Latin decem,
meaning “ten.” The decimal number system has
as its base the number 10.
We can represent the decimal number 12.61873
as follows:
This number is read “twelve and sixty-one thousand
eight hundred forty-three hundred-thousandths.”
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Decimals
Each place of
a decimal
may be
named by its
power of 10.
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Decimals as Concrete Materials
Suppose that a long in the base-ten block set
represents 1 unit (instead of letting the cube
represent 1 unit ). Then the cube represents
Copyright © 2013, 2010, and 2007, Pearson Education, Inc.
Decimals as Concrete Materials
To represent a decimal such as 2.235, we can
think of a block as a unit.
Copyright © 2013, 2010, and 2007, Pearson Education, Inc.
Example 7-1
Convert each of the following to decimals.
a.
2  10  5 2  10 5
5



 2
 2.5
10
10
10
10
b.
0.56
c.
0.0205
Copyright © 2013, 2010, and 2007, Pearson Education, Inc.
Example 7-2
Convert each of the following to decimals.
a.
b.
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Example 7-2
(continued)
c.
d.
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Terminating Decimals
Decimals that can be written with only a finite
number of places to the right of the decimal point
are called terminating decimals.
A rational number
in simplest form can be
written as a terminating decimal if, and only if,
the prime factorization of the denominator
contains no primes other than 2 or 5.
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Terminating Decimals
Can be written as
terminating decimals.
Cannot be written as
terminating decimals.
Copyright © 2013, 2010, and 2007, Pearson Education, Inc.
Ordering Terminating Decimals
A terminating decimal is easily located on a
number line because it can be represented as a
rational number , where b ≠ 0, and b is a power
of 10.
Copyright © 2013, 2010, and 2007, Pearson Education, Inc.
Comparing Terminating Decimals
Compare 0.67643 and 0.6759.
1. Line up the numbers by place value.
2. Start at the left and find the first place where
the face values are different.
3. Compare these digits. The number
containing the greater face value in this
place is the greater of the two numbers. The
digits in the thousandths place are different
and 6 > 5, so 0.67643 > 0.6759.
Copyright © 2013, 2010, and 2007, Pearson Education, Inc.