Basic Mathematics for College Students

1

that a block of digits repeats in the pattern shown. Repeating decimals can also be

written using a bar over the repeating block of digits. For example, 0.4444... can be

written as 0.4, and 1.373737... can be written as 1.37.

374 Chapter 4 Decimals

Some fractions can be written as decimals using an alternate approach. If the

denominator of a fraction in simplified form has factors of only 2’s or 5’s, or a

combination of both, it can be written as a decimal by multiplying it by a form of 1.

The objective is to write the fraction in an equivalent form with a denominator that is

a power of 10, such as 10, 100, 1,000, and so on.

EXAMPLE (^2) Write each fraction as a decimal using multiplication by a
form of 1: a. b.
StrategyWe will multiply by and we will multiply by.
WHYThe result of each multiplication will be an equivalent fraction with a
denominator that is a power of 10. Such fractions are then easy to write in decimal
form.
Solution
a.Since we need to multiply the denominator of by 2 to obtain a denominator 45
45 22 1140 2525

11

40

4

5

Self Check 2

Write each fraction as a decimal

using multiplication by a form

of 1:

a.

b.

Now TryProblems 27 and 29

8

25

2

5

of 10, it follows that should be the form of 1 that is used to build.

Multiply by 1 in the form of.

Write the fraction as a decimal.

b.Since we need to multiply the denominator of 1140 by 25 to obtain a denominator

0.8

Multiply the numerators.

Multiply the denominators.



8

10

2

2

4

(^5)

4

5



4

5



2

2

22 45

of 1,000, it follows that should be the form of 1 that is used to build.

Multiply by 1 in the form of.

0.275 Write the fraction as a decimal.

Multiply the numerators.

Multiply the denominators.



275

1,000

4011 2525

11

40



11

40



25

25

11

40

25

25

EXAMPLE (^3) Write the mixed number in decimal form.
StrategyWe need only find the decimal equivalent for the fractional part of the
mixed number.
WHYThe whole-number part in the decimal form is the same as the whole-
number part in the mixed number form.

5 167

Self Check 3

Write the mixed number

in decimal form.

Now TryProblem 37

(^3 1720)
Mixed numbers can also be written in decimal form.
Caution! When using an overbarto write a repeating decimal, use the least
number of digits necessary to show the repeating block of digits.

0.333.. .0.3 6.7454545.. .6.745

0.333.. .0.333 6.7454545.. .6.7454