Basic Mathematics for College Students

In parts a, b, and c of Example 1, the division process ended because a remainder
of 0 was obtained. When such a division terminateswith a remainder of 0, we call the
resulting decimal a terminating decimal.Thus, 0.75, 0.625, and 3.5 are three examples
of terminating decimals.

4.5 Fractions and Decimals 373

We can check the result by writing 0.75 as a fraction in simplest form:

0.75 is seventy-five hundredths.

This is the original fraction.

b. means.

Thus,.

c. means.

Thus,^72 3.5.

Write a decimal point and one additional zero to the right of 7.

 The remainder is 0.

3.5

(^2)  7 .0
 6
10
 10
0
(^727)  2
5
8 0.625
Write a decimal point and three additional zeros to the right of 5.
 The remainder is 0.

0.625

(^8)  5 .000
 48
20
 16
40
 40
0
(^585)  8



3

4

To simplify the fraction, factor 75 as 3 25 and 100

 as 4 25 and remove the common factor of 25.

3  25

1

4  25

1

0.75

75

100

The Language of Mathematics To terminatemeans to bring to an end. In the

movie The Terminator,actor Arnold Schwarzenegger plays a heartless

machine sent to Earth to bring an end to his enemies.

2 Write fractions as equivalent repeating decimals.

Sometimes, when we are finding a decimal equivalent of a fraction, the division
process never gives a remainder of 0. In this case, the result is a repeating decimal.
Examples of repeating decimals are 0.4444... and 1.373737.... The three dots tell us

Caution! A common error when finding a decimal equivalent

for a fraction is to incorrectly divide the denominator by the

numerator.An example of this is shown on the right, where the

decimal equivalent of (a number less than 1) is incorrectly

found to be 1.6 (a number greater than 1).

58

1.6

5  8 .0

 5

30

 30

0