Basic Mathematics for College Students

This fraction represents the division problem. From this result, we have
the following observations.

• The division problem is equivalent to ; that is, they have
  the same answer.


• The decimal points in boththe divisor and the dividend of the first division
  problem have been moved two decimal places to the right to create the
  second division problem.

These observations illustrate the following rule for division with a decimal divisor.

0.360.2592 becomes (^36) 25.92
0.360.2592 (^36) 25.92
(^36) 25.92
4.4 Dividing Decimals 361
Division with a Decimal Divisor
To divide with a decimal divisor:

1. Write the problem in long division form.


2. Move the decimal point of the divisor so that it becomes a whole number.


3. Move the decimal point of the dividend the same number of places to the
   right.


4. Write the decimal point in the quotient (answer) directly above the
   decimal point in the dividend. Divide as if working with whole numbers.


5. If necessary, additional zeros can be written to the right of the last digit of
   the dividend to continue the division.

EXAMPLE 4

Divide:

StrategyWe will move the decimal point of the divisor, 0.36, two places to the
right and we will move the decimal point of the dividend, 0.2592, the same number
of places to the right.

WHYWe can then use the rule for dividing a decimal by a whole number.

SolutionWe begin by writing the problem in long division form.

Since the divisor is now a whole number, we can use the rule for dividing a decimal
by a whole number to find the quotient.

Now divide as with whole numbers.

Check:

Since this is the dividend, the result checks.

0.72

 36

432

2160

25.92

0.72

36 25.92

 25 2

72

 72

0

Move the decimal point two places to the right in the divisor and

the dividend. Write the decimal point in the quotient (answer)

directly above the decimal point in the dividend.

.

0 360 25. 92

0.2592

0.36

Self Check 4

Divide:

Now TryProblem 27

0.6045

0.65