Basic Mathematics for College Students

4.4 Dividing Decimals 363

Success Tip To round a quotient to a certain decimal place value, continue

the division process one more column to its right to find the test digit.

Using Your CALCULATOR Dividing Decimals

The nucleus of a cell contains vital information about the cell in the form of

DNA. The nucleus is very small: A typical animal cell has a nucleus that is only

0.00023622 inch across. How many nuclei (plural of nucleus) would have to be

laid end to end to extend to a length of 1 inch?

To find how many 0.00023622-inch lengths there are in 1 inch, we must use

division:.

1 .00023622

On some calculators, we press the key to display the quotient.

It would take approximately 4,233 nuclei laid end to end to extend to a length

of 1 inch.

ENTER

  4233.3418

1 0.00023622

4 Estimate quotients of decimals.

There are many ways to make an error when dividing decimals. Estimation is a helpful
tool that can be used to determine whether or not an answer seems reasonable.
To estimate quotients, we use a method that approximates both the dividend and
the divisor so that they divide easily. There is one rule of thumb for this method: If
possible, round both numbers up or both numbers down.

Self Check 6

Estimate the quotient:

Now TryProblems 35 and 39

6,229.24968.9

5 Divide decimals by powers of 10.

To develop a set of rules for division of decimals by a power of 10, we consider the
problems and.

Move the decimal points in the divisor

and dividend one place to the right.

81.3

0 1 (^) 81.3
 8
1
 1
3
 3
0
Write a zero to the
right of the 3.

0.813

(^10) 8.13 0
 8 0
13
 10
30
 30
0

8.13 10 8.130.1

 



EXAMPLE (^6) Estimate the quotient:
StrategyWe will round the dividend and the divisor down and find.
WHYThe division can be made easier if the dividend and the divisor end with
zeros. Also, 40 divides 240 exactly.
Solution
To divide, drop one zero from 240
and from 40, and find 24 4.
The estimate is 6.
If we calculate , the quotient is exactly 5.77. Note that the
estimate is close: It’s just 0.23 more than 5.77.

248.68743.1

248.68743.1 240  40  6

240  40

248.68743.1

The dividend is

approximately

The divisor is

approximately