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0 . 8215199 ÷ 4 . 113 size 12{0 "." "8215199" div 4 "." "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 4 12 3 can be checked by multiplying 4 and 3, we can check our division by performing the multiplication

4.113 3 decimal places × 0.1997373 7 decimal places

This multiplication produces 3 + 7 = 10 size 12{3+7="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.

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Practice set c

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

42 . 49778 ÷ 14 . 261 size 12{"42" "." "49778" div "14" "." "261"} {}

2.98

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0 . 001455 ÷ 0 . 291 size 12{0 "." "001455" div 0 "." "291"} {}

0.005

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7 . 459085 ÷ 2 . 1192 size 12{7 "." "459085" div 2 "." "1192"} {}

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

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Dividing decimals by powers of 10

In problems 4 and 5 of [link] , we found the decimal representations of 8, 162 . 41 ÷ 10 size 12{8,"162" "." "41" div "10"} {} and 8, 162 . 41 ÷ 100 size 12{8,"162" "." "41" div "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.

816.241 10 8162.410 80            ̲ 16          10          ̲ 62        60        ̲ 24      20      ̲ 41    40    ̲ 10  10  ̲

Thus, 8, 162 . 41 ÷ 10 = 816 . 241 size 12{8,"162" "." "41" div "10"="816" "." "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.

81.6241 100 8162.4100 800            ̲ 162          100          ̲ 62 4       60 0       ̲ 2 41     2 00     ̲ 410   400   ̲ 100 100 ̲ 0

Thus, 8, 162 . 41 ÷ 100 = 81 . 6241 size 12{8,"162" "." "41" div "100"="81" "." "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, 248 . 6 ÷ 100 size 12{9,"248" "." 6 div "100"} {}
Since there are 2 zeros in this power of 10, we move the decimal point 2 places to the left.

9248.6 divided by 100 is equal to 92.480. Notice that the only effect is the movement of a decimal two places to the left of 9248.6.

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3 . 28 ÷ 10 , 000 size 12{3 "." "28" div "10","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.

3.28 divided by 10,000 is equal to 0.000328. Notice that the only effect is the movement of a decimal four places to the left of 0003.28.

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Practice set d

Find the decimal representation of each quotient.

182 . 5 ÷ 10 size 12{"182" "." 5 div "10"} {}

18.25

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182 . 5 ÷ 100 size 12{"182" "." 5 div "100"} {}

1.825

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182 . 5 ÷ 1, 000 size 12{"182" "." 5 div 1,"000"} {}

0.1825

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182 . 5 ÷ 10 , 000 size 12{"182" "." 5 div "10","000"} {}

0.01825

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646 . 18 ÷ 100 size 12{"646" "." "18" div "100"} {}

6.4618

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21 . 926 ÷ 1, 000 size 12{"21" "." "926" div 1,"000"} {}

0.021926

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Exercises

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

4 . 8 ÷ 3 size 12{4 "." 8÷3} {}

1.6

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16 . 8 ÷ 8 size 12{"16" "." 8÷8} {}

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18 . 5 ÷ 5 size 12{"18" "." 5÷5} {}

3.7

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12 . 33 ÷ 3 size 12{"12" "." "33"÷3} {}

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54 . 36 ÷ 9 size 12{"54" "." "36"÷9} {}

6.04

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73 . 56 ÷ 12 size 12{"73" "." "56"÷"12"} {}

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159 . 46 ÷ 17 size 12{"159" "." "46"÷"17"} {}

9.38

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12 . 16 ÷ 64 size 12{"12" "." "16"÷"64"} {}

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37 . 26 ÷ 81 size 12{"37" "." "26"÷"81"} {}

0.46

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439 . 35 ÷ 435 size 12{"439" "." "35"÷"435"} {}

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36 . 98 ÷ 4 . 3 size 12{"36" "." "98"÷4 "." 3} {}

8.6

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46 . 41 ÷ 9 . 1 size 12{"46" "." "41"÷9 "." 1} {}

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3 . 6 ÷ 1 . 5 size 12{3 "." 6÷1 "." 5} {}

2.4

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0 . 68 ÷ 1 . 7 size 12{0 "." "68"÷1 "." 7} {}

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50 . 301 ÷ 8 . 1 size 12{"50" "." "301"÷8 "." 1} {}

6.21

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2 . 832 ÷ 0 . 4 size 12{2 "." "832"÷0 "." 4} {}

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4 . 7524 ÷ 2 . 18 size 12{4 "." "7524"÷2 "." "18"} {}

2.18

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16 . 2409 ÷ 4 . 03 size 12{"16" "." "2409"÷4 "." "03"} {}

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1 . 002001 ÷ 1 . 001 size 12{1 "." "002001"÷1 "." "001"} {}

1.001

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25 . 050025 ÷ 5 . 005 size 12{"25" "." "050025"÷5 "." "005"} {}

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12 . 4 ÷ 3 . 1 size 12{"12" "." 4÷3 "." 1} {}

4

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0 . 48 ÷ 0 . 08 size 12{0 "." "48"÷0 "." "08"} {}

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30 . 24 ÷ 2 . 16 size 12{"30" "." "24"÷2 "." "16"} {}

14

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48 . 87 ÷ 0 . 87 size 12{"48" "." "87"÷0 "." "87"} {}

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12 . 321 ÷ 0 . 111 size 12{"12" "." "321"÷0 "." "111"} {}

111

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64 , 351 . 006 ÷ 10 size 12{"64","351" "." "006"÷"10"} {}

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64 , 351 . 006 ÷ 100 size 12{"64","351" "." "006"÷"100"} {}

643.51006

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64 , 351 . 006 ÷ 1, 000 size 12{"64","351" "." "006"÷1,"000"} {}

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64 , 351 . 006 ÷ 1, 000 , 000 size 12{"64","351" "." "006"÷1,"000","000"} {}

0.064351006

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0 . 43 ÷ 100 size 12{0 "." "43"÷"100"} {}

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

11 . 2944 ÷ 6 . 24 size 12{"11" "." "2944"÷6 "." "24"} {}

Actual Quotient Tenths Hundredths Thousandths
Actual Quotient Tenths Hundredths Thousandths
1.81 1.8 1.81 1.810
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45 . 32931 ÷ 9 . 01 size 12{"45" "." "32931"÷9 "." "01"} {}

Actual Quotient Tenths Hundredths Thousandths
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3 . 18186 ÷ 0 . 66 size 12{3 "." "18186"÷0 "." "66"} {}

Actual Quotient Tenths Hundredths Thousandths
Actual Quotient Tenths Hundredths Thousandths
4.821 4.8 4.82 4.821
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4 . 3636 ÷ 4 size 12{4 "." "3636"÷4} {}

Actual Quotient Tenths Hundredths Thousandths
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0 . 00006318 ÷ 0 . 018 size 12{0 "." "00006318"÷0 "." "018"} {}

Actual Quotient Tenths Hundredths Thousandths
Actual Quotient Tenths Hundredths Thousandths
0.00351 0.0 0.00 0.004
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For the following 9 problems, find each solution.

Divide the product of 7.4 and 4.1 by 2.6.

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

0.01

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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.

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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

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Six cans of cola cost $2.58. What is the price of one can?

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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

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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?

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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

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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?

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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 . 8994 ÷ 2 . 01 size 12{3 "." "8994"÷2 "." "01"} {}

1.94

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0 . 067444 ÷ 0 . 052 size 12{0 "." "067444"÷0 "." "052"} {}

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14 , 115 . 628 ÷ 484 . 74 size 12{"14","115" "." "628"÷"484" "." "74"} {}

29.120

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219 , 709 . 36 ÷ 9941 . 6 size 12{"219","709" "." "36"÷"9941" "." 6} {}

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0 . 0852092 ÷ 0 . 49271 size 12{0 "." "0852092"÷0 "." "49271"} {}

0.173

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2 . 4858225 ÷ 1 . 11611 size 12{2 "." "4858225"÷1 "." "11611"} {}

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0 . 123432 ÷ 0 . 1111 size 12{0 "." "123432"÷0 "." "1111"} {}

1.111

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2 . 102838 ÷ 1 . 0305 size 12{2 "." "102838"÷1 "." "0305"} {}

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Exercises for review

( [link] ) Convert 4 7 8 size 12{4 { {7} over {8} } } {} to an improper fraction.

39 8

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( [link] ) 2 7 size 12{ { {2} over {7} } } {} of what number is 4 5 size 12{ { {4} over {5} } } {} ?

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( [link] ) Find the sum. 4 15 + 7 10 + 3 5 size 12{ { {4} over {"15"} } + { {7} over {"10"} } + { {3} over {5} } } {} .

47 30 or 1 17 30

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

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

2.8634

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Questions & Answers

I only see partial conversation and what's the question here!
Crow Reply
what about nanotechnology for water purification
RAW Reply
please someone correct me if I'm wrong but I think one can use nanoparticles, specially silver nanoparticles for water treatment.
Damian
what is the stm
Brian Reply
is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
Rafiq
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
Damian
How we are making nano material?
LITNING Reply
what is a peer
LITNING Reply
What is meant by 'nano scale'?
LITNING Reply
What is STMs full form?
LITNING
scanning tunneling microscope
Sahil
how nano science is used for hydrophobicity
Santosh
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
Rafiq
what is differents between GO and RGO?
Mahi
what is simplest way to understand the applications of nano robots used to detect the cancer affected cell of human body.? How this robot is carried to required site of body cell.? what will be the carrier material and how can be detected that correct delivery of drug is done Rafiq
Rafiq
what is Nano technology ?
Bob Reply
write examples of Nano molecule?
Bob
The nanotechnology is as new science, to scale nanometric
brayan
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Damian
Is there any normative that regulates the use of silver nanoparticles?
Damian Reply
what king of growth are you checking .?
Renato
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
Stoney Reply
why we need to study biomolecules, molecular biology in nanotechnology?
Adin Reply
?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
Adin
why?
Adin
what school?
Kyle
biomolecules are e building blocks of every organics and inorganic materials.
Joe
anyone know any internet site where one can find nanotechnology papers?
Damian Reply
research.net
kanaga
sciencedirect big data base
Ernesto
Introduction about quantum dots in nanotechnology
Praveena Reply
what does nano mean?
Anassong Reply
nano basically means 10^(-9). nanometer is a unit to measure length.
Bharti
do you think it's worthwhile in the long term to study the effects and possibilities of nanotechnology on viral treatment?
Damian Reply
absolutely yes
Daniel
how to know photocatalytic properties of tio2 nanoparticles...what to do now
Akash Reply
it is a goid question and i want to know the answer as well
Maciej
characteristics of micro business
Abigail
for teaching engĺish at school how nano technology help us
Anassong
How can I make nanorobot?
Lily
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
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Source:  OpenStax, Fundamentals of mathematics. OpenStax CNX. Aug 18, 2010 Download for free at http://cnx.org/content/col10615/1.4
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