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A division problem is shown. 0.8 is on the inside of the division sign, 4 is on the outside. Above the division sign is 0.2.

Notice that the decimal point in the quotient is directly above the decimal point in the dividend.

To divide a decimal by a whole number, we place the decimal point in the quotient above the decimal point in the dividend and then divide as usual. Sometimes we need to use extra zeros at the end of the dividend to keep dividing until there is no remainder.

Divide a decimal by a whole number.

  1. Write as long division, placing the decimal point in the quotient above the decimal point in the dividend.
  2. Divide as usual.

Divide: 0.12 ÷ 3 .

Solution

0.12 ÷ 3
Write as long division, placing the decimal point in the quotient above the decimal point in the dividend. .
Divide as usual. Since 3 does not go into 0 or 1 we use zeros as placeholders. .
0.12 ÷ 3 = 0.04
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Divide: 0.28 ÷ 4 .

0.07

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Divide: 0.56 ÷ 7 .

0.08

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In everyday life, we divide whole numbers into decimals—money—to find the price of one item. For example, suppose a case of 24 water bottles cost $3.99 . To find the price per water bottle, we would divide $3.99 by 24 , and round the answer to the nearest cent (hundredth).

Divide: $3.99 ÷ 24 .

Solution

$3.99 ÷ 24
Place the decimal point in the quotient above the decimal point in the dividend. .
Divide as usual. When do we stop? Since this division involves money, we round it to the nearest cent (hundredth). To do this, we must carry the division to the thousandths place. .
Round to the nearest cent. $0.166 $0.17
$3.99 ÷ 24 $0.17

This means the price per bottle is 17 cents.

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Divide: $6.99 ÷ 36 .

$0.19

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Divide: $4.99 ÷ 12 .

$0.42

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Divide a decimal by another decimal

So far, we have divided a decimal by a whole number. What happens when we divide a decimal by another decimal? Let’s look at the same multiplication problem we looked at earlier, but in a different way.

( 0.2 ) ( 4 ) = 0.8

Remember, again, that a multiplication problem can be rephrased as a division problem. This time we ask, “How many times does 0.2 go into 0.8 ?” Because ( 0.2 ) ( 4 ) = 0.8 , we can say that 0.2 goes into 0.8 four times. This means that 0.8 divided by 0.2 is 4 .

0.8 ÷ 0.2 = 4
A number line is shown with 0, 0.2, 0.4, 0.6, 0.8, and 1. There are braces showing a distance of 0.2 between each adjacent set of 2 numbers.

We would get the same answer, 4 , if we divide 8 by 2 , both whole numbers. Why is this so? Let’s think about the division problem as a fraction.

0.8 0.2 ( 0.8 ) 10 ( 0.2 ) 10 8 2 4

We multiplied the numerator and denominator by 10 and ended up just dividing 8 by 4 . To divide decimals, we multiply both the numerator and denominator by the same power of 10 to make the denominator a whole number. Because of the Equivalent Fractions Property, we haven’t changed the value of the fraction. The effect is to move the decimal points in the numerator and denominator the same number of places to the right.

We use the rules for dividing positive and negative numbers with decimals, too. When dividing signed decimals, first determine the sign of the quotient and then divide as if the numbers were both positive. Finally, write the quotient with the appropriate sign.

It may help to review the vocabulary for division:

a divided by b is shown with a labeled as the dividend and b labeled as the divisor. Then a over b is shown with a labeled as the divided and b labeled as the divisor. Then a is shown inside a division problem with b on the outside with a labeled as the dividend and b labeled as the divisor.

Divide decimal numbers.

  1. Determine the sign of the quotient.
  2. Make the divisor a whole number by moving the decimal point all the way to the right. Move the decimal point in the dividend the same number of places to the right, writing zeros as needed.
  3. Divide. Place the decimal point in the quotient above the decimal point in the dividend.
  4. Write the quotient with the appropriate sign.

Questions & Answers

how do they get the third part x = (32)5/4
kinnecy Reply
can someone help me with some logarithmic and exponential equations.
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sure. what is your question?
ninjadapaul
20/(×-6^2)
Salomon
okay, so you have 6 raised to the power of 2. what is that part of your answer
ninjadapaul
I don't understand what the A with approx sign and the boxed x mean
ninjadapaul
it think it's written 20/(X-6)^2 so it's 20 divided by X-6 squared
Salomon
I'm not sure why it wrote it the other way
Salomon
I got X =-6
Salomon
ok. so take the square root of both sides, now you have plus or minus the square root of 20= x-6
ninjadapaul
oops. ignore that.
ninjadapaul
so you not have an equal sign anywhere in the original equation?
ninjadapaul
Commplementary angles
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The answer is neither. The function, 2 = 0 cannot exist. Hence, the function is undefined.
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Kristine 2*2*2=8
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No. 7x -4y is simplified from 4x + (3y + 3x) -7y
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I start with an easy one. carbon nanotubes woven into a long filament like a string
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Yes, Nanotechnology has a very fast field of applications and their is always something new to do with it...
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In this morden time nanotechnology used in many field . 1-Electronics-manufacturad IC ,RAM,MRAM,solar panel etc 2-Helth and Medical-Nanomedicine,Drug Dilivery for cancer treatment etc 3- Atomobile -MEMS, Coating on car etc. and may other field for details you can check at Google
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At high concentrations (>0.01 M), the relation between absorptivity coefficient and absorbance is no longer linear. This is due to the electrostatic interactions between the quantum dots in close proximity. If the concentration of the solution is high, another effect that is seen is the scattering of light from the large number of quantum dots. This assumption only works at low concentrations of the analyte. Presence of stray light.
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the Beer law works very well for dilute solutions but fails for very high concentrations. why?
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Source:  OpenStax, Prealgebra. OpenStax CNX. Jul 15, 2016 Download for free at http://legacy.cnx.org/content/col11756/1.9
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