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5.1

Rational Numbers

Now

B E F O R E

W H Y ?

You wrote decimals and

You’ll write fractions as

So you can assess a recycling

Vocabulary

fractions.

decimals and vice versa.

plan, as in Ex. 45.

rational number,

p. 219

terminating decimal,

A

rational number

is a number that

p. 219

Rational numbers

can be written as a quotient of two

repeating decimal,

Integers

p. 219

integers. Whole numbers and integers

are part of the set of rational numbers,

Whole

as shown in the Venn diagram.

numbers

Example 1

Identifying Rational Numbers

Show that the number is rational by writing it as a quotient of two

integers.

3

1

a. 7

b.

10

c. 5

d.

3

4

2

Solution

7

a. Write the integer 7 as

.

1

10

10

b. Write the integer 10 as

or

. These fractions are equivalent.

1

1

3

2

3

c. Write the mixed number 5

as the improper fraction

.

4

4

Review Help

1

1

1

7

d. Think of 3

as the opposite of 3

. First write 3

as

. Then you

2

2

2

2

For help with writing mixed

1

7

7

numbers as improper

can write

3

as

. To write

as a quotient of two integers,

2

2

2

fractions, see p. 778.

you can assign the negative sign to either the numerator or the

7

7

denominator. You can write

or

.

2

2

If you take a rational number in the

Terminating and Repeating Decimals

a

form

and carry out the division of a by b, the quotient will be either a

b

terminating decimal or a repeating decimal. In a

terminating decimal

,

the division ends because you obtain a final remainder of zero. In a

repeating decimal

, a digit or block of digits in the quotient repeats

without end. Example 2 on page 220 shows how to write both a

terminating decimal and a repeating decimal.

219

Lesson 5.1

Rational Numbers

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