# 8.4 Decimals: division of decimals  (Page 3/3)

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$0\text{.}\text{8215199}÷4\text{.}\text{113}$

 Display Reads Type .8215199 0.8215199 Press ÷ 0.8215199 Type 4.113 4.113 Press = 0.1997373

There are EIGHT DIGITS — DISPLAY FILLED! BE AWARE OF POSSIBLE APPROXI­MATIONS.

We can check for a possible approximation in the following way. Since the division $\stackrel{3}{4\overline{)12}}$ can be checked by multiplying 4 and 3, we can check our division by performing the multiplication

$\underset{\text{places}}{\underset{\text{3 decimal}}{\underbrace{4.113}}}×\underset{\text{places}}{\underset{\text{7 decimal}}{\underbrace{0.1997373}}}$

This multiplication produces $3+7=\text{10}$ decimal digits. But our suspected quotient contains only 8 decimal digits. We conclude that the answer is an approximation. Then, rounding to five decimal places, we get 0.19974.

## Practice set c

Find each quotient using a calculator. If the result is an approximation, round to four decimal places.

$\text{42}\text{.}\text{49778}÷\text{14}\text{.}\text{261}$

2.98

$0\text{.}\text{001455}÷0\text{.}\text{291}$

0.005

$7\text{.}\text{459085}÷2\text{.}\text{1192}$

3.5197645 is an approximate result. Rounding to four decimal places, we get 3.5198

## Dividing decimals by powers of 10

In problems 4 and 5 of [link] , we found the decimal representations of $8,\text{162}\text{.}\text{41}÷\text{10}$ and $8,\text{162}\text{.}\text{41}÷\text{100}$ . Let's look at each of these again and then, from these observations, make a general statement regarding division of a decimal num­ber by a power of 10.

Thus, $8,\text{162}\text{.}\text{41}÷\text{10}=\text{816}\text{.}\text{241}$ .

Notice that the divisor 10 is composed of one 0 and that the quotient 816.241 can be obtained from the dividend 8,162.41 by moving the decimal point one place to the left.

Thus, $8,\text{162}\text{.}\text{41}÷\text{100}=\text{81}\text{.}\text{6241}$ .

Notice that the divisor 100 is composed of two 0's and that the quotient 81.6241 can be obtained from the dividend by moving the decimal point two places to the left.

Using these observations, we can suggest the following method for dividing decimal numbers by powers of 10.

## Dividing a decimal fraction by a power of 10

To divide a decimal fraction by a power of 10, move the decimal point of the decimal fraction to the left as many places as there are zeros in the power of 10. Add zeros if necessary.

## Sample set d

Find each quotient.

$9,\text{248}\text{.}6÷\text{100}$
Since there are 2 zeros in this power of 10, we move the decimal point 2 places to the left.

$3\text{.}\text{28}÷\text{10},\text{000}$

Since there are 4 zeros in this power of 10, we move the decimal point 4 places to the left. To do so, we need to add three zeros.

## Practice set d

Find the decimal representation of each quotient.

$\text{182}\text{.}5÷\text{10}$

18.25

$\text{182}\text{.}5÷\text{100}$

1.825

$\text{182}\text{.}5÷1,\text{000}$

0.1825

$\text{182}\text{.}5÷\text{10},\text{000}$

0.01825

$\text{646}\text{.}\text{18}÷\text{100}$

6.4618

$\text{21}\text{.}\text{926}÷1,\text{000}$

0.021926

## Exercises

For the following 30 problems, find the decimal representation of each quotient. Use a calculator to check each result.

$4\text{.}8÷3$

1.6

$\text{16}\text{.}8÷8$

$\text{18}\text{.}5÷5$

3.7

$\text{12}\text{.}\text{33}÷3$

$\text{54}\text{.}\text{36}÷9$

6.04

$\text{73}\text{.}\text{56}÷\text{12}$

$\text{159}\text{.}\text{46}÷\text{17}$

9.38

$\text{12}\text{.}\text{16}÷\text{64}$

$\text{37}\text{.}\text{26}÷\text{81}$

0.46

$\text{439}\text{.}\text{35}÷\text{435}$

$\text{36}\text{.}\text{98}÷4\text{.}3$

8.6

$\text{46}\text{.}\text{41}÷9\text{.}1$

$3\text{.}6÷1\text{.}5$

2.4

$0\text{.}\text{68}÷1\text{.}7$

$\text{50}\text{.}\text{301}÷8\text{.}1$

6.21

$2\text{.}\text{832}÷0\text{.}4$

$4\text{.}\text{7524}÷2\text{.}\text{18}$

2.18

$\text{16}\text{.}\text{2409}÷4\text{.}\text{03}$

$1\text{.}\text{002001}÷1\text{.}\text{001}$

1.001

$\text{25}\text{.}\text{050025}÷5\text{.}\text{005}$

$\text{12}\text{.}4÷3\text{.}1$

4

$0\text{.}\text{48}÷0\text{.}\text{08}$

$\text{30}\text{.}\text{24}÷2\text{.}\text{16}$

14

$\text{48}\text{.}\text{87}÷0\text{.}\text{87}$

$\text{12}\text{.}\text{321}÷0\text{.}\text{111}$

111

$\text{64},\text{351}\text{.}\text{006}÷\text{10}$

$\text{64},\text{351}\text{.}\text{006}÷\text{100}$

643.51006

$\text{64},\text{351}\text{.}\text{006}÷1,\text{000}$

$\text{64},\text{351}\text{.}\text{006}÷1,\text{000},\text{000}$

0.064351006

$0\text{.}\text{43}÷\text{100}$

For the following 5 problems, find each quotient. Round to the specified position. A calculator may be used.

$\text{11}\text{.}\text{2944}÷6\text{.}\text{24}$

 Actual Quotient Tenths Hundredths Thousandths
 Actual Quotient Tenths Hundredths Thousandths 1.81 1.8 1.81 1.810

$\text{45}\text{.}\text{32931}÷9\text{.}\text{01}$

 Actual Quotient Tenths Hundredths Thousandths

$3\text{.}\text{18186}÷0\text{.}\text{66}$

 Actual Quotient Tenths Hundredths Thousandths
 Actual Quotient Tenths Hundredths Thousandths 4.821 4.8 4.82 4.821

$4\text{.}\text{3636}÷4$

 Actual Quotient Tenths Hundredths Thousandths

$0\text{.}\text{00006318}÷0\text{.}\text{018}$

 Actual Quotient Tenths Hundredths Thousandths
 Actual Quotient Tenths Hundredths Thousandths 0.00351 0.0 0.00 0.004

For the following 9 problems, find each solution.

Divide the product of 7.4 and 4.1 by 2.6.

Divide the product of 11.01 and 0.003 by 2.56 and round to two decimal places.

0.01

Divide the difference of the products of 2.1 and 9.3, and 4.6 and 0.8 by 0.07 and round to one decimal place.

A ring costing $567.08 is to be paid off in equal monthly payments of$46.84. In how many months will the ring be paid off?

12.11 months

Six cans of cola cost $2.58. What is the price of one can? A family traveled 538.56 miles in their car in one day on their vacation. If their car used 19.8 gallons of gas, how many miles per gallon did it get? 27.2 miles per gallon Three college students decide to rent an apartment together. The rent is$812.50 per month. How much must each person contribute toward the rent?

A woman notices that on slow speed her video cassette recorder runs through 296.80 tape units in 10 minutes and at fast speed through 1098.16 tape units. How many times faster is fast speed than slow speed?

3.7

A class of 34 first semester business law students pay a total of \$1,354.90, disregarding sales tax, for their law textbooks. What is the cost of each book?

## Calculator problems

For the following problems, use calculator to find the quotients. If the result is approximate (see Sample Set C [link] ) round the result to three decimal places.

$3\text{.}\text{8994}÷2\text{.}\text{01}$

1.94

$0\text{.}\text{067444}÷0\text{.}\text{052}$

$\text{14},\text{115}\text{.}\text{628}÷\text{484}\text{.}\text{74}$

29.120

$\text{219},\text{709}\text{.}\text{36}÷\text{9941}\text{.}6$

$0\text{.}\text{0852092}÷0\text{.}\text{49271}$

0.173

$2\text{.}\text{4858225}÷1\text{.}\text{11611}$

$0\text{.}\text{123432}÷0\text{.}\text{1111}$

1.111

$2\text{.}\text{102838}÷1\text{.}\text{0305}$

## Exercises for review

( [link] ) Convert $4\frac{7}{8}$ to an improper fraction.

$\frac{39}{8}$

( [link] ) $\frac{2}{7}$ of what number is $\frac{4}{5}$ ?

( [link] ) Find the sum. $\frac{4}{\text{15}}+\frac{7}{\text{10}}+\frac{3}{5}$ .

$\frac{47}{30}$ or $1\frac{17}{30}$

( [link] ) Round 0.01628 to the nearest ten-thousandths.

( [link] ) Find the product (2.06)(1.39)

2.8634

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