Page 346 - Basic College Mathematics with Early Integers

S E C T I O N 4.5 I FRACTIONS, DECIMALS, AND ORDER OF OPERATIONS 323

Notice that the digit 2 keeps occurring as the remainder.This will continue so that
the digit 6 will keep repeating in the quotient. We place a bar over the digit 6 to
indicate that it repeats.
2
= 0.666 Á= 0.6
3
2 2
We can also write a decimal approximation for . For example, rounded to the
3 3
2
nearest hundredth is 0.67.This can be written as L 0.67.
3

Work Practice 3

22 22
Example 4 Write as a decimal. (Recall that the fraction is an approxi- PRACTICE 4
7 7
mation for ) Round to the nearest hundredth.p. Write 28 as a decimal. Round
13
to the nearest thousandth.
Solution: 3.142 L 3.14 Carry the division out to the thousandths place.
722.000
-21
10
-7
30
-28
20
-14
6
22
The fraction in decimal form is approximately 3.14.
7

Work Practice 4

3
Example 5 Write 2 as a decimal. PRACTICE 5
16
5
Solution: Write 3 16 as a decimal.
3
Option 1. Write the fractional part Option 2. Write 2 as an improper
16
only as a decimal. fraction, and divide.
0.1875 2.1875
3 3 35
163.0000 2 = 1635.0000
16 16 16
-16 -32
1 40 3 0
-1 28 -1 6
120 1 40
-112 -1 28
80 120
-80 -112
0 80
3 -80
Thus 2 =2.1875
16 0

Answers
Work Practice 5
4. 2.154 5. 3.3125