Basic Mathematics for College Students

4.5 Fractions and Decimals 375

SolutionTo write as a fraction, we find.

Since the whole-number part of the decimal must be the same as the whole-number
part of the mixed number, we have:

We would have obtained the same result if we changed to the improper fraction

(^8716) and divided 87 by 16.

5 167

5

7

16

5.4375

Write a decimal point and four additionl zeros to the right of 7.

 The remainder is 0.

0.4375

(^16)  7 .0000
 64
60
 48
120
 112
80
 80
0

167 7 ^16

EXAMPLE (^4) Write as a decimal.
StrategyWe will divide the numerator of the fraction by its denominator and
watch for a repeating pattern of nonzero remainders.
WHYOnce we detect a repeating pattern of remainders, the division process can
stop.
Solution means.
We can use three dots to show that a repeating pattern of 6’s appears in the quotient:
Or, we can use an overbar to indicate the repeating part (in this case, only the 6),
and write the decimal equivalent in more compact form:
5
12

0.416

5

12

0.416666...

Write a decimal point and four additional zeros to the right of 5.

It is apparent that 8 will continue to reappear as the remainder. Therefore,

6 will continue to reappear in the quotient. Since the repeating pattern is

now clear, we can stop the division.

0.4166

(^12) 5.0000
4 8
20
 12
80
 72
80
 72
8

125 5 ^12

5

12

Self Check 4

Write as a decimal.

Now TryProblem 41

1

12

EXAMPLE (^5) Write as a decimal.
StrategyTo find the decimal equivalent for  116 , we will first find the decimal

 116

Self Check 5

Write as a decimal.

Now TryProblem 47

 (^1333)
equivalent for. To do this, we will divide the numerator of by its denominator
and watch for a repeating pattern of nonzero remainders.
6
11
6
11
     
cc