Division of Decimal Numbers

🏆Practice dividing decimal fractions

To divide decimal numbers, we will carry out the following steps:

First step - We will make the decimal point in the dividend (the number we want to divide) disappear by moving it to the right the necessary number of places until it is completely "gone".
Second step - In the divisor (the second number in the operation, that is, the number by which it is divided) we will move the decimal point to the right the same number of places that we moved the first number (even if this number of steps is not enough to make it disappear)
Third step - We will solve the "new" exercise (with the "new" numbers).

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Test yourself on dividing decimal fractions!

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\( 4.2:0.1= \)

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Division of Decimal Numbers

Dividing decimal numbers is a bit more complicated than dividing whole numbers, but, if you follow these steps in order, we're sure you'll manage!
Objective: The elimination of the decimal point from the dividend.
In division exercises of decimal numbers, we can elegantly eliminate the decimal point...
All we have to do is shift it to the right the same number of places in both numbers.


What does it mean?

Let's look at the exercise 1.6:0.4= 1.6:0.4= 
We will always first focus on the dividend – In our exercise the 1.61.6
To make the decimal point "disappear" we should move it to the right by one place.
We move it and obtain 1616.
Let's not forget to perform the same operation on the divisor 0.40.4
Observe - If in the dividend we have moved the decimal point only one place to the right, also in the divisor the point can take only one step.
The number of places the decimal point is moved must be identical in both numbers!

We do it and obtain 44
The new exercise we now have is 16:4=16:4=
And its result, clearly, is 44. The same result as our original exercise.
You wonder how can this be?
As long as we have carried out the same operation on both numbers in the exercise, it is valid, and the exercise doesn't really change, but is represented in a different way.


Another exercise

0.25:0.05=0.25:0.05=

Solution:
We will proceed step by step:
We will focus on the dividend 0.250.25
Let's see. How many places do we need to move the decimal point to the right for it to "disappear"? 22 steps
We will move it two steps and obtain 2525
Now let's do the same with the divisor 0.050.05
Let's move the decimal point 22 steps to the right and we will obtain 55
Our new exercise is: 25:5=525:5=5


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Exercise for advanced level

0.36:0.6=0.36:0.6=
Solution:
We will focus on the dividend 0.360.36
Let's ask, how many steps to the right must the decimal point move to disappear? Two steps.
Let's move it 22 steps to the right and we will get 3636.
Now let's do it with the divisor 0.60.6
Move the decimal point 22 steps to the right.
Attention! We know it's very tempting to move it only one step and get to 66 but that would be a huge mistake!
We must move the point the same number of steps as we have moved it in the dividend for the result to be correct.
Let's move the decimal point two places and we will get 6060.

Our new exercise will be 36:60=36:60=
We will obtain: 36/6036/60
Let's simplify, we will get: 6/10=3/56/10 = 3/5


Another exercise

0.7:1=0.7:1=

Solution
Let's proceed according to the rules we have learned:
We will focus on removing the decimal point from the dividend 0.70.7
We will move the decimal point one place to the right and obtain 77
Now, let's move to the divisor 11.
Note: The original number does not have a decimal point, but we will add it and then place several zeros to not change its value.
We will consider 11 as 1.01.0
Now, let's move the decimal point one place to the right and we will obtain 1010
Our new exercise is 7:107:10
We can leave it as is, as a fraction 7/107/10 or else, solve it according to the rules of long division.


Examples and exercises with solutions for dividing decimal numbers

Exercise #1

4.2:0.1= 4.2:0.1=

Video Solution

Answer

42 42

Exercise #2

0.36:0.1= 0.36:0.1=

Video Solution

Answer

3.6 3.6

Exercise #3

3.36:0.1= 3.36:0.1=

Video Solution

Answer

33.6 33.6

Exercise #4

1.3:0.1= 1.3:0.1=

Video Solution

Answer

13 13

Exercise #5

0.7:0.1= 0.7:0.1=

Video Solution

Answer

7 7

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