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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

where we get a research paper on Nano chemistry....?
Maira Reply
what are the products of Nano chemistry?
Maira Reply
There are lots of products of nano chemistry... Like nano coatings.....carbon fiber.. And lots of others..
learn
Even nanotechnology is pretty much all about chemistry... Its the chemistry on quantum or atomic level
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da
no nanotechnology is also a part of physics and maths it requires angle formulas and some pressure regarding concepts
Bhagvanji
hey
Giriraj
Preparation and Applications of Nanomaterial for Drug Delivery
Hafiz Reply
revolt
da
Application of nanotechnology in medicine
what is variations in raman spectra for nanomaterials
Jyoti Reply
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
yes that's correct
Professor
I think
Professor
Nasa has use it in the 60's, copper as water purification in the moon travel.
Alexandre
nanocopper obvius
Alexandre
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
if virus is killing to make ARTIFICIAL DNA OF GRAPHENE FOR KILLED THE VIRUS .THIS IS OUR ASSUMPTION
Anam
analytical skills graphene is prepared to kill any type viruses .
Anam
Any one who tell me about Preparation and application of Nanomaterial for drug Delivery
Hafiz
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
how did you get the value of 2000N.What calculations are needed to arrive at it
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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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