Basic Mathematics for College Students

362 Chapter 4 Decimals

Success Tip When dividing decimals, moving the decimal points the same

number of places to the right in boththe divisor and the dividend does not

change the answer.

3 Round a decimal quotient.

In Example 4, the division process stopped after we obtained a 0 from the second

subtraction. Sometimes when we divide, the subtractions never give a zero remainder,

and the division process continues forever. In such cases, we can round the result.

EXAMPLE 5

Divide:. Round the quotient to the nearest hundredth.

StrategyWe will use the methods of this section to divide to the thousandths

column.

WHYTo round to the hundredths column, we need to continue the division

process for one more decimal place, which is the thousandths column.

SolutionWe begin by writing the problem in long division form.

We need to write two zeros to the right of the last digit of the dividend so that we

can divide to the thousandths column.

After dividing to the thousandths column, we round to the hundredths column.

The rounding digit in the hundredths column is 5.

The test digit in the thousandths column is 7.

The division process can stop. We have divided to the thousandths column.

Since the test digit 7 is 5 or greater, we will round 13.357 up to approximate the

quotient to the nearest hundredth.

Read as “is approximately equal to.”

Check:

Since this is close to the original dividend, 9.35, the result seems reasonable.

13.36

 0.7

9.352

9.35

0.7

13.36

.

7 93.5 00

To write the divisor as a whole number, move the decimal point one place

to the right. Do the same for the dividend. Place the decimal point in the

quotient (answer) directly above the decimal point in the dividend.

.

0 7 93. 5

9.35

0.7

Self Check 5

Divide:. Round

the quotient to the nearest

hundredth.

Now TryProblem 33

12.820.9

 

13.357

7 93.5 00

 7

23

 21

25

 21

40

 35

50

 49

1

The approximation of the quotient

The original divisor