1. 7 Chapter Decimals: Rational Numbers and Percent
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2. 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)
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3. 7-1 Introduction to Decimals
Representations of Decimals
Ordering Terminating Decimals
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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 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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6. 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
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7. Decimals as Concrete Materials
To represent a decimal such as 2.235, we can think of a block as a unit.
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Example 7-1
Convert each of the following to decimals. a. b.
0.56 c.
0.0205
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Example 7-2
Convert each of the following to decimals. a. b.
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Example (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.
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13. 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.
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14. Comparing Terminating Decimals
Compare and
Line up the numbers by place value.
Start at the left and find the first place where the face values are different.
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 >
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