Basic Mathematics for College Students

Written in order from smallest to largest, we have :

, 2.168,

20

9

2

1

6

380 Chapter 4 Decimals

To make the comparison of the three decimals easier, we stack them as shown

below.

2.1680 This is 2.168 with an additional 0.

2.1666 ... This is.

2.2222 ... This is.^209

2 61 2.16

Working from left to right, this is

the first column in which the

digits differ. Since 2 1, it

follows that is

the largest of the three numbers.

2.222.. .^209

Working from left to right, this is the

first column in which the top two

numbers differ. Since 8 6, it follows

that 2.168 is the next largest number

and that 2.16 2 61 is the smallest.

6 Evaluate expressions containing fractions and decimals.

Expressions can contain both fractions and decimals. In the following examples, we

show two methods that can be used to evaluate expressions of this type. With the first

method we find the answer by working in terms of fractions.

EXAMPLE (^10) Evaluate by working in terms of fractions.
StrategyWe will begin by writing 0.27 as a fraction.
WHYThen we can use the methods of Chapter 3 for adding fractions with unlike
denominators to find the sum.
SolutionTo write 0.27 as a fraction, it is helpful to read it aloud as “twenty-seven
hundredths.”
Replace 0.27 with.
The LCD for and is 300. To build each
fraction so that its denominator is 300,
multiply by a form of 1.
Multiply the numerators.
Multiply the denominators.
Add the numerators and write the sum over
 the common denominator 300.

181

300



100

300



81

300

27

100

1

^13

3



100

100



27

100



3

3

27

(^100)

1

3

0.27

1

3



27

100

1

3 0.27

Self Check 10

Evaluate by working in terms of

fractions:

Now TryProblem 79

0.53^16

Now we will evaluate the expression from Example 10 by working in terms of

decimals.

EXAMPLE (^11) Estimate by working in terms of decimals.
StrategySince 0.27 has two decimal places, we will begin by finding a decimal
approximation for to two decimal places.
WHYThen we can use the methods of this chapter for adding decimals to find the
sum.
1
3
1
3 0.27
Self Check 11
Estimate the result by working in
terms of decimals:
Now TryProblem 87

0.53^16