Basic Mathematics for College Students

402 Chapter 4 Decimals

To checkthe result, we multiply the divisor by the

quotient. The result should be the dividend.

Check:

The check confirms that 6.2 4 1.55.

Quotient

Divisor

Dividend

1.55

 4

6.20

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 a 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.

Divide:

Write the problem in long division form. Move the decimal

point of the divisor, 3.4, one place to the right to make it

a whole number. Move the decimal point of the dividend,

1.462, the same number of places to the right.

Now use the rule for dividing a decimal by a whole number.

Write a decimal point in the quotient (answer) directly

above the decimal point in the dividend.

Divide as with whole numbers.

0. 4 3

34  14. 6 2

 13 6

1 0 2

 1 0 2

0

3.4 1.462

1.462

3.4

Sometimes when we divide decimals, the

subtractions never give a zero remainder, and the

division process continues forever. In such cases,

we can round the result.

Divide:. Round the quotient to the nearest hundredth.

To round to the hundredths column, we need to continue the

division process for one more decimal place, which is the

thousandths column.

Rounding digit: hundredths column

Test digit: Since 8 is 5 or greater, add 1

to the rounding digit and drop the test digit.

Thus,0.77 6 0.13.

0.128

(^6) 0.77 0
 6
17
 12
50
 48
2

0.77 6

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.

Estimate the quotient:

To divide, drop one zero from

320 and one zero from 20,

and then find 322.

The estimate is 16. (The exact answer is 14.2.)

337.9623.8 320  20  16

337.9623.8

Dividing a decimal by 10, 100, 1,000, and so on

To find the quotient of a decimal and 10, 100,

1,000, and so on, move the decimal point to the left

the same number of places as there are zeros in

the power of 10.

Divide:

Since the divisor 10,000 has four

zeros, move the decimal point four

places to the left. Insert two

placeholder zeros (shown in blue).

79.3610,0000. 007936

79.3610,000



 

The remainder is still not 0.















The dividend is

approximately

The divisor is

approximately