Basic Mathematics for College Students

4.5 Fractions and Decimals 381

SolutionWe have seen that the decimal equivalent of is the repeating decimal
0.333....Rounded to the nearest hundredth:.

Approximate with the decimal 0.33.

0.60 Do the addition.

0.3

1

3

 0.27

0.60

1

(^3)

1

3

0.270.330.27

1

3 0.33

1

3

In Examples 10 and 11, we evaluated^13 0.27in different ways. In Example 10,
we obtained the exact answer,^181300. In Example 11, we obtained an approximation, 0.6.

The results seem reasonable when we write^181300 in decimal form:^181300 0.60333....

EXAMPLE 12

Evaluate:

StrategyWe will find the decimal equivalent of and then evaluate the
expression in terms of decimals.

WHYIts easier to perform multiplication and addition with the given decimals
than it would be converting them to fractions.

SolutionWe use division to find the decimal equivalent of.

Write a decimal point and one additional zero to the right of the 4.

Now we use the order of operation rule to evaluate the expression.

Replace with its decimal equivalent, 0.8.

Evaluate: (0.5)^2 0.25.

Do the multiplication: (0.8)(1.35) 1.08.

1.33 Do the addition.

1.080.25

(0.8)(1.35)0.25

4

(0.8)(1.35)(0.5) 5

2

a

4

5

b(1.35)(0.5)^2

0.8

(^5) 4.0
 4 0
0
4
5
4
5
a

4

5

b(1.35)(0.5)^2

Self Check 12

Evaluate:

Now TryProblem 99

(0.6)^2 (2.3)a

1

8

b

1.0

1

8

 0.25

1.33

1

2

.3

4

5

 0.8

1.080

0

2

.5

0.5

0.25

7 Solve application problems involving fractions and decimals.

EXAMPLE (^13) Shopping A shopper purchased^3 pound of fruit, priced
4
Self Check 13
DELICATESSENSA shopper
purchased pound of Swiss
cheese, priced at $2.19 per
pound, and pound of sliced
turkey, selling for $6.40 per
pound. Find the total cost of
these items.
Now TryProblem 111
3
4
2
3
at $0.88 a pound, and pound of fresh-ground coffee, selling for $6.60 a pound.
Find the total cost of these items.
Analyze

• pound of fruit was purchased at $0.88 per pound. Given


• pound of coffee was purchased at $6.60 per pound. Given


• What was the total cost of the items? Find

Form To find the total cost of each item, multiply the number of pounds purchased
by the price per pound.

1

3

3

4

1

3