Decimals are part of our life, from prices to other current operations, so it is essential to know how to operate with decimals. We all know that you can always use a calculator to perform a division with decimals, but basic calculations and those a little more advanced such as divisions with decimals are part of the minimum culture that every person should know, besides who knows what. It can get you in trouble to perform a quick division with decimals if you don’t have a calculator at that time.
On the other hand, we must point out that as long as we make calculations using our head and not the calculator, we will be developing brain capacities, and we will not let our brain go to sleep.
If you want to learn how to divide with decimals, pay attention to the following article as we explain how to carry out the steps to achieve division with decimals correctly.
First of all, it should be noted that there are different types of division with decimals, let’s see each type below:
Division of a decimal number
In this case we want to divide a decimal number in the dividend by an integer.
First we will see and treat the dividend as if it were an integer. We’ll forget for a moment that there’s a comma marking the decimals.
After you are done with normal division we will count how many decimal numbers are after the comma. And taking this into account we will go to the quotient and counting from the end of the number we will put the comma where it coincides with the number of decimal numbers that we counted before.
46.77 : 3
16 15.59
1 7
27
0
Quotient with decimals
We obtain a quotient with decimals in the event that the dividend is less than the divisor, it will be the only way to solve this division. We will also take decimals in divisions in which we want to continue dividing the number until we get the maximum number of decimals possible.
For example, if we want to divide 4 by 8, four in the dividend is less than 8 in the divisor. To begin to carry out the division we are going to add a 0 next to the 4, and in the quotient we will write a 0 and a comma.
40 : 8
0,
Next we will follow the division as if it were a normal division.
40 : 8
– 40 0.5
——–
0
Now we are going to see a specific case in which the remainder is not zero, for this we are going to add a zero in the remainder and we will continue with the division normally. We can continue adding zeros to the remainders until it finally gives zero.
Let’s see an example:
50 : 8
20 0.625
40
0
Division of a whole number by a decimal number
Next we are going to see how we are going to divide an integer number by a decimal number.
First we are going to remove the decimals from the divisor number and leave it as a whole number. We must count the decimals that the divisor number has before transforming it.
Then we are going to go to the divisor and at the end of the number we will add as many zeros as decimal numbers had the number of the divisor.
And with this last step we can divide as always. Here we see an example:
187 : 4.25 would become à 18700 : 425
Let’s do the division as normal:
18700 : 425
1700 44
0
Divide a decimal number by another decimal number
In this case we must make a transformation on the divisor. We will count the decimals again and take them into account for later, we will remove the comma and leave the whole number.
Next we will move on to the dividend number. In this case we are going to move the comma as many times to the right as decimal numbers had the divisor before transforming it.
In the event that the dividend does not have enough decimal numbers to roll the decimal point the number of times necessary, in this case we will add as many zeros as necessary to roll the decimal point. In the end we will obtain an integer ending in zero and without commas, since leaving a comma followed by zero is invalid, and the comma must be removed directly.
Let’s see an example to clarify how a decimal number is divided by another decimal number.
We’ll start with this division:
18,247 : 4.25
We will change the divisor by removing the comma and leaving a whole number (we count two decimal places). Then we will roll the comma two places to the right in the dividend number (it is equivalent to the two decimal places that we subtracted from the divisor). This is the result of the new division:
1824.7: 425
If it had been the case that the initial dividend number had been 1824.7, with a single decimal place, the new division number would have been 182470.
Once we have made the initial changes we can do the division as normal:
1824.7 : 425
124 7 4.2
39.7
Divide a decimal number by 10, 100, 1000
In the event that you have to divide a decimal number by a number that is a multiple of 10, you should not worry, you just have to rewrite the dividend number. Then count how many zeros the divisor has and we will roll the decimal point of the dividend to the left as many positions as zeros we have counted.
Let’s see some examples:
33.8 : 10 we start by writing the whole number and then we move the comma one position further to the left because the divisor has only one zero. The result will be: 3.38
125.6 : 1000 we will write the dividend number again, then we will count how many zeros there are in the divisor, in this case there are three. Well now we will roll the comma three positions to the left. In this case we will obtain the following result, 1256. Being at the beginning of the number means that this number does not have an integer part and we must put a zero in front of the comma, leaving: 0.1256.
And if we have more zeros in the divisor number than whole numbers in the dividend number, what do we do? Since we cannot shift the comma to the left as many positions as there are zeros in the divisor.
Well, in this case we will write the dividend number and then we will roll the comma according to the number of zeros that there are in the divisor. When we get to the point where there are no more whole numbers left, then we will add a zero for each missing whole number until we roll the comma all the necessary positions.
Let’s look at an example of this specific situation to clarify it a bit more:
For example, we have the division 15.89 : 1000, we are going to copy the dividend first: 15.89, we will count how many zeros there are in the number of the divisor, in this case there are three.
Since the dividend 15.89 only has two integers, we can only roll the comma two positions to the left, so we have one more position to roll. We are going to add a zero to complete the third position that we were missing. Since there are no more integers, we will put a zero in front of the comma. This will be the result:
15.89 : 1000 = 0.01589
Learn how to divide with decimals, here we have shown you what you should do in each particular case, as you can see, it is not that complicated either, we just have to keep in mind what should be done in each case with commas, zeros, etc.