Learning Outcomes

Divide a decimal by a entirety numberDivide a decimal by an additional decimalDivide a totality number by a decimal

Just just like multiplication, department of decimal is really much like separating whole numbers. We just have actually to number out wherein the decimal point must be placed.To understand decimal division, let’s take into consideration the multiplication problem

\left(0.2\right)\left(4\right)=0.8Remember, a multiplication problem can it is in rephrased together a division problem. For this reason we can write

0.8\div 4=0.2We have the right to think the this together “If we divide 8 one per 10 into 4 groups, how plenty of are in each group?” The number line below shows that there are 4 groups that two-tenths in eight-tenths. Therefore 0.8\div 4=0.2.

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Notice that the decimal allude in the quotient is directly over the decimal suggest in the dividend.To division a decimal by a whole number, we location the decimal suggest in the quotient above the decimal suggest in the dividend and then divide as usual. Sometimes we have to use extra zeros in ~ the end of the dividend come keep splitting until over there is no remainder.


Divide a decimal by a entirety number.

Write as long division, placing the decimal suggest in the quotient above the decimal allude in the dividend.Divide together usual.

example

Divide: 0.12\div 3.

Solution

0.12\div 3
Write as lengthy division, put the decimal point in the quotient above the decimal suggest in the dividend.
0.12\div 3=0.04

try it


Watch teh following video clip to see an additional example of how to division a totality number by a decimal.


example

In day-to-day life, we divide entirety numbers into decimals—money—to uncover the price that one item. For example, mean a situation of 24 water bottles price $3.99. To discover the price every water bottle, we would certainly divide $3.99 by 24, and round the answer come the nearest cent (hundredth).

Divide: $3.99\div 24.


Show Solution

Solution

.99 separated by 24. The very first step says, " data-label="">
$3.99\div 24
Place the decimal suggest in the quotient above the decimal point in the dividend.
Round to the nearest cent.$0.166\approx $0.17
$3.99\div 24\approx $0.17

This method the price per party is 17 cents.


Divide a Decimal by another Decimal

So far, us have divided a decimal by a totality number. What happens when we division a decimal by an additional decimal? let’s look in ~ the very same multiplication problem we looked at earlier, however in a various way.

\left(0.2\right)\left(4\right)=0.8Remember, again, that a multiplication problem can be rephrased together a division problem. This time we ask, “How plenty of times walk 0.2 get in 0.8\text?"" since \left(0.2\right)\left(4\right)=0.8, we can say the 0.2 goes into 0.8 4 times. This way that 0.8 separated by 0.2 is 4.

0.8\div 0.2=4


Divide decimal numbers

Determine the authorize of the quotient.Make the divisor a entirety number by relocating the decimal allude all the means to the right. Relocate the decimal point in the dividend the same number of places to the right, creating zeros together needed.Divide. Ar the decimal allude in the quotient over the decimal allude in the dividend.Write the quotient through the proper sign.

example

Divide: -2.89\div \text(3.4\text).


Show Solution

Solution

Determine the sign of the quotient.The quotient will be negative.
Make the divisor the entirety number by ‘moving’ the decimal point all the way to the right. ‘Move’ the decimal allude in the dividend the same variety of places to the right.
Write the quotient with the ideal sign.-2.89\div \left(3.4\right)=-0.85

Solution

-25.65\div \left(-0.06\right)
The signs are the same.The quotient is positive.
Make the divisor a whole number through ‘moving’ the decimal point all the means to the right.

‘Move’ the decimal point in the dividend the same number of places.

Write the quotient with the appropriate sign.-25.65\div \left(-0.06\right)=427.5

Solution

4\div 0.05
The signs are the same.The quotient is positive.
Make the divisor a whole number through ‘moving’ the decimal allude all the way to the right.

Move the decimal suggest in the dividend the same variety of places, including zeros together needed.

Write the quotient through the proper sign.

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4\div 0.05=80
We deserve to relate this example to money. How plenty of nickels are there in 4 dollars? since 4\div 0.05=80, there space 80 nickels in $4.