Basic Mathematics for College Students

4.5 Fractions and Decimals 379

EXAMPLE (^9) Write the numbers in order from smallest to largest:
2.168, ,
StrategyWe will write and in decimal form.
WHYThen we can do a column-by-column comparison of the numbers to
determine the largest and smallest.
SolutionFrom the number line on page 378, we see that. Thus,.
To write as a decimal, we divide 20 by 9.
Thus,^209 2.222....

2.222

9 20.000

 18

20

 18

20

 18

20

 18

2

20

9

(^16) 0.16 2 16 2.16
20
(^2 9)
1
6

20

9

2

1

6

Self Check 9

Write the numbers in order from

smallest to largest: 1.832, ,

Now TryProblem 75

(^95 1 56)
Write a decimal point and three additional zeros to the right of 20.
To make the comparison of the decimals easier, we can write one zero
after 8 so that they have the same number of digits to the right of the decimal
point.

0. 8 0 This is the decimal equivalent for.
   0.91

As we work from left to right, this is the first column in which the digits differ.

Since , it follows that is less than 0.91, and we can write.

b.In Example 6, we saw that To make the comparison of these
repeating decimals easier, we write them so that they have the same number of
digits to the right of the decimal point.
0.3 5 55... This is.
0.3 3 33... This is.

As we work from left to right, this is the first column in which the digits differ.

Since , it follows that is greater than , and

we can write.

c.To write as a decimal, we divide 9 by 4.

Write a decimal point and two additional zeros to the right of 9.

From the division, we see that^94 2.25.

2.25

(^4) 9.00
 8
10
 8
20
 20
0
9
4

0.35^13

5  3 0.3555.. .0.35 0.3333.. . 31

1

3

0.35

1

3 0.3333....

4

0.80 5 0.91

4

8  (^95)
4
5