Basic Mathematics for College Students

358 Chapter 4 Decimals

SECTION 4.4

Dividing Decimals

In Chapter 1, we used a process called long division to divide whole numbers.

Long division form

Divisor

In this section, we consider division problems in which the divisor, the dividend, or

both are decimals.

Quotient

Dividend

Remainder

2

(^5)  10
10
0

1 Divide a decimal by a whole number.
To develop a rule for decimal division, let’s consider the problem. If we
rewrite the division as , we can use the long division method from Chapter 3 for
changing an improper fraction to a mixed number to find the answer:
Here the result is written in quotient  form.
To perform this same division using decimals, we write 47 as 47.0 and divide as we
would divide whole numbers.
Since , either method gives the same answer. This result suggests the
following method for dividing a decimal by a whole number.

4 107 4.7

Note that the decimal point in the quotient (answer) is placed

directly above the decimal point in the dividend.

After subtracting 40 from 47, bring down the 0 and continue to divide.

The remainder is 0.

4.7

10 47.0

 40

7 0

 7 0

0

remainder

divisor

4

7

10

10  47

 40

7

47

10

47  10

Dividing a Decimal by a Whole Number

To divide a decimal by a whole number:

1. Write the problem in long division form and place a decimal point in the
   quotient (answer) directly above the decimal point in the dividend.


2. Divide as if working with whole numbers.


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

EXAMPLE (^1) Divide:. Check the result.
StrategySince the divisor, 6, is a whole number, we will write the problem in long
division form and place a decimal point directly above the decimal point in 42.6.
Then we will divide as if the problem was 426  6.

42.6 6

Self Check 1

Divide:. Check the

result.

Now TryProblem 15

20.8 4

Objectives

1 Divide a decimal by a whole

number.

2 Divide a decimal by a decimal.

3 Round a decimal quotient.

4 Estimate quotients of decimals.

5 Divide decimals by powers of 10.

6 Divide signed decimals.

7 Use the order of operations

rule.

8 Evaluate formulas.

9 Solve application problems by

dividing decimals.