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432 100 10 = 432 100 10 10 1 1 = 432 1 10 1 = 432 10 = 43 2 10 = 43.2

We have converted the division 4 . 32 ÷ 1 . 8 size 12{4 "." "32" div 1 "." 8} {} into the division 43 . 2 ÷ 18 size 12{"43" "." 2 div "18"} {} , that is,

1.8 4.32 18 43.2

Notice what has occurred.


4.32 divided by 1.8. The decimal place in both numbers is moved to the right by one space.

If we "move" the decimal point of the divisor one digit to the right, we must also "move" the decimal point of the dividend one place to the right. The word "move" actually indicates the process of multiplication by a power of 10.

Method of dividing a decimal by a decimal number

To divide a decimal by a nonzero decimal,
  1. Convert the divisor to a whole number by moving the decimal point to the position immediately to the right of the divisor's last digit.
  2. Move the decimal point of the dividend to the right the same number of digits it was moved in the divisor.
  3. Set the decimal point in the quotient by placing a decimal point directly above the newly located decimal point in the dividend.
  4. Divide as usual.

Sample set b

Find the following quotients.

32 . 66 ÷ 7 . 1 size 12{"32" "." "66" div 7 "." 1} {}

7.1 32.66


Long division. 32.66 divided by 7.1. Move the decimal place to the right for both numbers, making 326.6 divided by 71. 71 goes into 326 4 times, with a remainder of 42. Bring down the 6. 71 goes into 426 6 times, with a remainder of zero. The quotient is 4.6

  • The divisor has one decimal place.
  • Move the decimal point of both the divisor and the dividend 1 place to the right.
  • Set the decimal point.
  • Divide as usual.

Thus, 32 . 66 ÷ 7 . 1 = 4 . 6 size 12{"32" "." "66" div 7 "." 1=4 "." 6} {} .

Check: 32 . 66 ÷ 7 . 1 = 4 . 6 size 12{"32" "." "66" div 7 "." 1=4 "." 6} {} if 4 . 6 × 7 . 1 = 32 . 66 size 12{4 "." 6 times 7 "." 1="32" "." "66"} {}

4.6 × 7.1 ̲ 46 322    ̲ 32.66 True.

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1 . 0773 ÷ 0 . 513 size 12{1 "." "0773" div 0 "." "513"} {}

Long division. 1.0773 divided by .513. Move the decimal place three spaces to the right. 513 goes into 1077 twice, with a remainder of 51. Bring down the 3. 513 goes into 513 exactly once. The quotient is 2.1.

  • The divisor has 3 decimal places.
  • Move the decimal point of both the divisor and the dividend 3 places to the right.
  • Set the decimal place and divide.

Thus, 1 . 0773 ÷ 0 . 513 = 2 . 1 size 12{1 "." "0773" div 0 "." "513"=2 "." 1} {} .

Checking by multiplying 2.1 and 0.513 will convince us that we have obtained the correct result. (Try it.)

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12 ÷ 0 . 00032 size 12{"12" div 0 "." "00032"} {}

0.00032 12.00000

  • The divisor has 5 decimal places.
  • Move the decimal point of both the divisor and the dividend 5 places to the right. We will need to add 5 zeros to 12.
  • Set the decimal place and divide.

12 divided by 0.00032. The decimal place needs to be moved five spaces to the right, which means that five zeros need to be added to the right of the 12 to perform the subtraction.
This is now the same as the division of whole numbers.

37500. 32 1200000. 96          ̲ 240        224        ̲ 160      160      ̲ 000

Checking assures us that 12 ÷ 0 . 00032 = 37 , 500 size 12{"12" div 0 "." "00032"="37","500"} {} .

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Practice set b

Find the decimal representation of each quotient.

9 . 176 ÷ 3 . 1 size 12{9 "." "176" div 3 "." 1} {}

2.96

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5 . 0838 ÷ 1 . 11 size 12{5 "." "0838" div 1 "." "11"} {}

4.58

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16 ÷ 0 . 0004 size 12{"16" div 0 "." "0004"} {}

40,000

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8, 162 . 41 ÷ 10 size 12{8,"162" "." "41" div "10"} {}

816.241

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8, 162 . 41 ÷ 100 size 12{8,"162" "." "41" div "100"} {}

81.6241

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8, 162 . 41 ÷ 1, 000 size 12{8,"162" "." "41" div 1,"000"} {}

8.16241

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8, 162 . 41 ÷ 10 , 000 size 12{8,"162" "." "41" div "10","000"} {}

0.816241

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Calculators

Calculators can be useful for finding quotients of decimal numbers. As we have seen with the other calculator operations, we can sometimes expect only approximate results. We are alerted to approximate results when the calculator display is filled with digits. We know it is possible that the operation may produce more digits than the calculator has the ability to show. For example, the multiplication

0.12345 5 decimal places × 0.4567 4 decimal places

produces 5 + 4 = 9 size 12{5+4=9} {} decimal places. An eight-digit display calculator only has the ability to show eight digits, and an approximation results. The way to recognize a possible approximation is illustrated in problem 3 of the next sample set.

Sample set c

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

12 . 596 ÷ 4 . 7 size 12{"12" "." "596" div 4 "." 7} {}

Display Reads
Type 12.596 12.596
Press ÷ 12.596
Type 4.7 4.7
Press = 2.68

Since the display is not filled, we expect this to be an accurate result.

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0 . 5696376 ÷ 0 . 00123 size 12{0 "." "5696376" div 0 "." "00123"} {}

Display Reads
Type .5696376 0.5696376
Press ÷ 0.5696376
Type .00123 0.00123
Press = 463.12

Since the display is not filled, we expect this result to be accurate.

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Questions & Answers

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
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it is a goid question and i want to know the answer as well
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characteristics of micro business
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for teaching engĺish at school how nano technology help us
Anassong
Do somebody tell me a best nano engineering book for beginners?
s. Reply
there is no specific books for beginners but there is book called principle of nanotechnology
NANO
what is fullerene does it is used to make bukky balls
Devang Reply
are you nano engineer ?
s.
fullerene is a bucky ball aka Carbon 60 molecule. It was name by the architect Fuller. He design the geodesic dome. it resembles a soccer ball.
Tarell
what is the actual application of fullerenes nowadays?
Damian
That is a great question Damian. best way to answer that question is to Google it. there are hundreds of applications for buck minister fullerenes, from medical to aerospace. you can also find plenty of research papers that will give you great detail on the potential applications of fullerenes.
Tarell
what is the Synthesis, properties,and applications of carbon nano chemistry
Abhijith Reply
Mostly, they use nano carbon for electronics and for materials to be strengthened.
Virgil
is Bucky paper clear?
CYNTHIA
carbon nanotubes has various application in fuel cells membrane, current research on cancer drug,and in electronics MEMS and NEMS etc
NANO
so some one know about replacing silicon atom with phosphorous in semiconductors device?
s. Reply
Yeah, it is a pain to say the least. You basically have to heat the substarte up to around 1000 degrees celcius then pass phosphene gas over top of it, which is explosive and toxic by the way, under very low pressure.
Harper
Do you know which machine is used to that process?
s.
how to fabricate graphene ink ?
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for screen printed electrodes ?
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s. Reply
of graphene you mean?
Ebrahim
or in general
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in general
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Graphene has a hexagonal structure
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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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