Page 334 - Basic College Mathematics with Early Integers

S E C T I O N 4.4 I DIVIDING DECIMALS 311

Example 3 Divide: -5.98 , 115 PRACTICE 3
Divide and check.
Solution: Recall that a negative number divided by a positive number gives a
a. -13.62 , 12
negative quotient.
b. -2.808 , (-104)
0.052
1155.980 ; Insert one 0.
-5 75
230
-230
0
Thus -5.98 , 115 =-0.052.

Work Practice 3

If the divisor is not a whole number, before we divide we need to move the dec-
imal point to the right until the divisor is a whole number.

1.564.85
divisor dividend

To understand how this works, let’s rewrite

64.85
1.564.85 as
1.5
10 10
and then multiply by 1 in the form of . We use the form so that the denominator
(divisor) becomes a whole number. 10 10

#
64.85 = 64.85 # 1= 64.85 # 10 = 64.85 10 = 648.5 ,
#
1.5 1.5 1.5 10 1.5 10 15

which can be written as 15.648.5. Notice that

1.564.85 is equivalent to 15.648.5

The decimal points in the dividend and the divisor were both moved one place to
the right, and the divisor is now a whole number. This procedure is summarized
next:

Dividing by a Decimal

Step 1: Move the decimal point in the divisor to the right until the divisor is a
whole number.

Step 2: Move the decimal point in the dividend to the right the same number of
places as the decimal point was moved in Step 1.
Step 3: Divide. Place the decimal point in the quotient directly over the moved
decimal point in the dividend.

Answers
3. a. -1.135 b. 0.027