7 Chapter 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.

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.” Copyright © 2013, 2010, and 2007, Pearson Education, Inc.

Copyright © 2013, 2010, and 2007, Pearson Education, Inc. Decimals Each place of a decimal may be named by its power of 10. Copyright © 2013, 2010, and 2007, Pearson Education, Inc.

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.

Copyright © 2013, 2010, and 2007, Pearson Education, Inc. Example 7-1 Convert each of the following to decimals. a. b. 0.56 c. 0.0205 Copyright © 2013, 2010, and 2007, Pearson Education, Inc.

Copyright © 2013, 2010, and 2007, Pearson Education, Inc. Example 7-2 Convert each of the following to decimals. a. b. Copyright © 2013, 2010, and 2007, Pearson Education, Inc.

Copyright © 2013, 2010, and 2007, Pearson Education, Inc. Example 7-2 (continued) c. d. Copyright © 2013, 2010, and 2007, Pearson Education, Inc.

Copyright © 2013, 2010, and 2007, Pearson Education, Inc. 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. Copyright © 2013, 2010, and 2007, Pearson Education, Inc.

Copyright © 2013, 2010, and 2007, Pearson Education, Inc. 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. 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 0.67643 > 0.6759. Copyright © 2013, 2010, and 2007, Pearson Education, Inc.