Basic Mathematics for College Students

350 Chapter 4 Decimals

Solution

a. The base is 2.4 and the exponent is 2. Write the base

as a factor 2 times.

Multiply the decimals.

b. The base is 0.05 and the exponent is 2.

Write the base as a factor 2 times.

Multiply the decimals. The product of two

decimals with like signs is positive.

0.0025

0.05

 0.05

0.0025

(0.05)^2 (0.05)(0.05)

5.76

(2.4)^2 2.42.4

5 Use the order of operations rule.

Recall that the order of operations rule is used to evaluate expressions that involve

more than one operation.

EXAMPLE (^9) Evaluate:
StrategyThe absolute value bars are grouping symbols. We will perform the
addition within them first.
WHYBy the order of operations rule, we must perform all calculations within
parentheses and other grouping symbols (such as absolute value bars) first.
Solution
Do the addition within the absolute
value symbols. Use the rule for adding
two decimals with different signs.
Simplify:.
Evaluate: (0.6)^2 0.36.
Do the multiplication: 5(1.7) 8.5.
Use the rule for adding two decimals
with different signs.

8.14

0.368.5

0.365(1.7)

(0.6)^2 5(1.7) 0 1.7 0 1.7

(0.6)^2  50 1.7 0

(0.6)^2  50 3.61.9 0

(0.6)^2  50 3.61.9 0

Self Check 9

Evaluate:

Now TryProblem 49

 20 4.45.6 0 (0.8)^2

6 Evaluate formulas.

Recall that to evaluate a formula, we replace the letters (called variables) with specific

numbers and then use the order of operations rule.

EXAMPLE (^10) Evaluate the formula for and
.
StrategyIn the given formula, we will replace the letter rwith 6 and hwith 3.1.
WHYThen we can use the order of operations rule to find the value of the
expression on the right side of the symbol.
Solution
6.28r(hr) means 6.28 r(hr).
Replace rwith 6 and hwith 3.1.
Do the addition within the parentheses.
Do the multiplication: 6.28(6) 37.68.
342.888 Do the multiplication.

37.68(9.1)

6.28(6)(9.1)

6.28( 6 )(3.1 6 )

S6.28r (hr)



r 6

S6.28r(hr) h3.1

Self Check 10

Evaluate for

and.

Now TryProblem 53

p3.14 r 3

V1.3pr^3

2.4

 2.4

96

480

5.76

37.68

 9.1

3768

339120

342.888

3

2

.6

16

 1.9

1.7

1

3

.7

 5

8.5

8.5

4

0

10

0.36

8.14