Basic Mathematics for College Students

1

112. Explain why multiplying by the form of 1 shown
     below moves the decimal points in the dividend,
     4.86, and the divisor, 0.2, one place to the right.
     4.86
     0.2



4.86

0.2



10

10

4.86

0.2 REVIEW

113. a. Find the GCF of 10 and 25.
     b. Find the LCM of 10 and 25.


114. a. Find the GCF of 8, 12, and 16.
     b. Find the LCM of 8, 12, and 16.

372 Chapter 4 Decimals

SECTION 4.5

Fractions and Decimals

In this section, we continue to explore the relationship between fractions and decimals.

1 Write fractions as equivalent terminating decimals.

A fraction and a decimal are said to be equivalentif they name the same number.

Every fraction can be written in an equivalent decimal form by dividing the numerator

by the denominator, as indicated by the fraction bar.

Writing a Fraction as a Decimal

To write a fraction as a decimal, divide the numerator of the fraction by its

denominator.

EXAMPLE (^1) Write each fraction as a decimal.
a. b. c.
StrategyWe will divide the numerator of each fraction by its denominator. We
will continue the division process until we obtain a zero remainder.
WHYWe divide the numerator by the denominator because a fraction bar
indicates division.
Solution
a. means. To find , we begin by writing it in long division form as

. To proceed with the division, we must write the dividend 3 with a decimal
point and some additional zeros. Then we use the procedure from Section 4.4
for dividing a decimal by a whole number.

Thus, 43 0.75. We say that the decimal equivalentof 34 is 0.75.

Write a decimal point and two additional zeros to the right of 3.

 The remainder is 0.

0.75

4  3 .00

2 8

20

 20

0

(^4)  3
(^34 3)  4 3  4

7

2

5

8

3

4

Self Check 1

Write each fraction as a decimal.

a.

b.

c.

Now TryProblems 15, 17, and 21

9

2

3

16

1

2

T

Objectives

1 Write fractions as equivalent

terminating decimals.

2 Write fractions as equivalent

repeating decimals.

3 Round repeating decimals.

4 Graph fractions and decimals

on a number line.

5 Compare fractions and

decimals.

6 Evaluate expressions

containing fractions and

decimals.

7 Solve application problems

involving fractions and

decimals.