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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

List and explain four factors of production
Vuyo Reply
capital labour entrepreneur natural resources
Thembi
What is supply
Ogodo Reply
when the supply decreases demand also decreases
Thembi
types of demand and the explanation
akin Reply
what is demand
akin Reply
other things remaining same if demend is increases supply is also decrease and if demend is decrease supply is also increases is called the demand
Mian
if the demand increase supply also increases
Thembi
you are wrong this is the law of demand and not the definition
Tarasum
Demand is the willingness of buy and ability to buy in a specific time period in specific place. Mian you are saying law of demand but not in proper way. you have to keep studying more. because its very basic things in Economics.
Hamza
Demand is the price of Quantity goods and services in which consumer's are willing and able to offer at a price in the market over a period of time
Umar
Demand is the quantity of goods and services that the consumer are willing and able to buy at a alternative prices over a given period of time. But mind you demand is quite different from need and want.
Tarasum
Demand can be defined as the graphical representation between price&demand
alkasim
sorry demand is nt a graphical representation between price and quantity demand but instead that is demand curve.
Ebrima
Demand is the willingness and ability of a consumer to buy a quantity of a good over a given period of time assuming all other things remain constant.
Vedaant
what is commercialization?
Doris Reply
How to talk loan for bank?
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Ritisha Reply
Answer: GPA stands for Grade Point Average. It is a standard way of measuring academic achievement in the U.S. Basically, it goes as follows: Each course is given a certain number of "units" or "credits", depending on the content of the course.
Yusuf
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Dansofo
founder , that is Adam Smith
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The wealth of Nations
Yusuf Reply
the wealth of nations, is it the first?
Umar
Yes very sure it was released in 1759
Yusuf
thank you Yusuf.
Umar
then when did he died?
Umar
17 July 1790 Born: 16 June 1723, Kirkcaldy, United Kingdom Place of death: Panmure House, Edinburgh, United Kingdom
Yusuf
1790
Yusuf
that's my today questions, thank you Yusuf it's bed time see u after.
Umar
what is fiscal policy
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what's mode?
Umar Reply
mode is the highest occurring frequency in a distribution
Bola
mode is the most commonly occurring item in a set of data.
Umar
Please, what is the difference between monopoly and monopsony?
Olaleye Reply
is there monopsony word?
Umar
I have no idea though
Umar
please, in which year Adam smith was born?
Umar
monopsony is when there's only one buyer while monopoly is when there's only one producer.
Bola
who have idea on Banter
Ibrahim
like trade by barter?
Bola
Monopoly is when there's excessively one seller and there is no entry in the market while monopsony is when there is one buyer
kemigisha
Adam smith was born in 1723
Bola
 (uncountable) Good humoured, playful, typically spontaneous conversation. verb (intransitive) To engage in banter or playful conversation. (intransitive) To play or do something amusing. (transitive) To tease mildly.
Umar
which book Adam smith published first? the first book of Adam smith pls.
Umar
wealth on nation, 1776
Daniel
what is market power and how can it affect an economy?
Gab Reply
market power:- where a firm is said to be a price setter.market power benefits the powerful at the expense of others.
Umar
Market power refers to the ability of a firm (or group of firms) to raise and maintain price above the level that would prevail under competition is referred to as market or monopoly power. The exercise of market power leads to reduced output and loss of economic welfare
Kartheek
find information about the national budget
Molahlegi
three branches of economics in which tourism is likely to figure
Makgotso Reply
What are those three branches?
IlRegno
Difference between extinct and extici spicies
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in a comparison of the stages of meiosis to the stage of mitosis, which stages are unique to meiosis and which stages have the same event in botg meiosis and mitosis
Leah Reply
Researchers demonstrated that the hippocampus functions in memory processing by creating lesions in the hippocampi of rats, which resulted in ________.
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7hours 36 min - 4hours 50 min
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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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