Page 315 - Basic College Mathematics with Early Integers

292 C HAPTE R 4 I DECIMALS

PRACTICE 10 Example 10 Add or subtract as indicated.Then estimate to see if the answer
is reasonable by rounding the given numbers and adding or
Add or subtract as indicated.
subtracting the rounded numbers.
Then estimate to see if the
answer is reasonable by
a. 27.6 + 519.25
rounding the given numbers
and adding or subtracting the Exact Estimate 1 Estimate 2
rounded numbers. 1
27.60 rounds to 30 30
a. 48.1 + 326.97 +519.25 rounds to +500 or +520
b. 18.09 - 0.746 546.85 530 550
Since the exact answer is close to either estimate, it is reasonable. (In the first
estimate, each number is rounded to the place value of the leftmost digit. In the
second estimate, each number is rounded to the nearest ten.)
b. 11.01 - 0.862
Exact Estimate 1 Estimate 2
9 10
0 10 0 10

1 1 . 0 1 0 rounds to 10 11
- 0 . 8 6 2 rounds to - 1 or - 1
9
1 0 . 1 4 8 10
In the first estimate, we rounded the first number to the nearest ten and the sec-
ond number to the nearest one. In the second estimate, we rounded both num-
Remember that
bers to the nearest one. Both estimates show us that our answer is reasonable.
estimates are used for our
convenience to quickly check Work Practice 10
the reasonableness of an
answer. Concept Check Why shouldn’t the sum 21.98 + 42.36 be estimated as
30 + 50 = 80?

Objective Using Decimals as Replacement Values

Let’s review evaluating expressions with given replacement values. This time the
replacement values are decimals.
PRACTICE 11
Evaluate y - z for y = 11.6 Example 11 Evaluate x - y for x = 2.8 and y = 0.92.
and z = 10.8.
Solution: Replace x with 2.8 and y with 0.92 and simplify.
PRACTICE 12
x - y = 2.8 - 0.92 2.80
Find the total monthly cost of
owning and operating a certain = 1.88 -0.92
automobile given the expenses 1.88
shown.
Work Practice 11
Monthly car
payment: $563.52 Objective Solving Problems by Adding or
Monthly Subtracting Decimals
insurance cost: $52.68
Average gasoline Decimals are very common in real-life problems.
bill per month: $127.50
Example 12 Calculating the Cost of Owning an Automobile
Answers
10. a. Exact: 375.07 b. Exact: 17.344 Find the total monthly cost of owning and operating a certain automobile given Copyright 2012 Pearson Education, Inc.
11. 0.8 12. $743.70 the expenses shown.
Monthly car payment: $256.63
Concept Check Answer
Monthly insurance cost: $47.52
Each number is rounded incorrectly.
The estimate is too high. Average gasoline bill per month: $95.33