Working around with decimals may be a little taxing, and when students are faced with the question of how to divide decimals, they realize that they have to exercise their brain more than ever before. However, taking a step-by-step approach to the problem in hand can make dividing decimals easy. Here is how …
Decimals are used to provide greater precision to the numerical value of a quantity. Along with this benefit comes a challenge, which is carrying out mathematical operations that are more difficult with decimals as compared to whole numbers. When it comes to dividing decimals, then the scenario becomes all the more complicated. It is so because division is the most complex function among all the four basic operations in mathematics. In fact, one needs to use successive subtraction to carry out a division. But problem-solving, which involves division of decimals, can be made easy by ensuring that the divisor is a whole number. This can be done by shifting the decimal, so that the divisor becomes a whole number. However, the dividend also needs to be altered and balanced accordingly to get an accurate result. This is the case if the divisor is a decimal. First let us learn how to divide a decimal when the divisor is a whole number.
This is the easier of the two cases for dividing decimals. When the divisor is a whole number and the dividend is a decimal, then ignore the decimal point of the dividend. Now, the problem becomes a simple one, which is a division involving whole numbers only. Work out the problem using the regular, long division method. Once the quotient is achieved, place a decimal point with as many numbers to the right, as it originally was in the dividend. Let’s understand this process with an example:
Let’s say, we have to solve 7.9/4 to find its quotient. Follow these steps for solving the problem:
- Step 1: Ignore the decimal point in the dividend. Now you have to divide 79/4.
- Step 2: Carry out the division with the regular long division method. The answer is 19.75.
- Step 3: The dividend had one digit to the right of the decimal point. So, we have to ensure that we shift the decimal, so that there is one more digit to its right. Hence, the answer is 1.975.
Let us see a few examples using the same division method.
Here the dividend is a decimal number while the divisor is 6. To make the division easy, we will initially ignore the decimal point and carry out the usual long division.
| 14 | |
| 6) | 84 |
| 6 | |
| 24 | |
| 24 | |
| 0 |
6: Divisor
84: Dividend
14: Quotient
0: Remainder
But we had to divide 8.4 by 6. Now, after the usual long division, the final step is to place the decimal. Since in the dividend, there is only one digit after the decimal, the quotient will also have only one digit after the decimal.
| 1.4 | |
| 6) | 8.4 |
Here the dividend is a decimal number, while the divisor is 2, which is a whole number.
| 48 | |
| 2) | 96 |
| 8 | |
| 16 | |
| 16 | |
| 0 |
2: Divisor
96: Dividend
48: Quotient
0: Remainder
Now, as there is only one digit after the decimal, the quotient will also have only one digit after the decimal.
| 4.8 | |
| 2) | 9.6 |
Here the dividend is a decimal number, while the divisor is 2, which is a whole number.
| 72 | |
| 2) | 144 |
| 0 | |
| 14 | |
| 14 | |
| 04 | |
| 4 | |
| 0 |
2: Divisor
144: Dividend
72: Quotient
0: Remainder
Now, as there is only one digit after the decimal, the quotient will also have only one digit after the decimal.
| 7.2 | |
| 2) | 14.4 |
Here the dividend is a decimal number, while the divisor is 11, which is a whole number.
| 49 | |
| 11) | 539 |
| 0 | |
| 53 | |
| 44 | |
| 99 | |
| 99 | |
| 0 |
11: Divisor
539: Dividend
49: Quotient
0: Remainder
Now, as there are two digits after the decimal, the quotient will also have two digits after the decimal.
| 0.49 | |
| 11) | 5.39 |
Here the dividend is a decimal number, while the divisor is 17, which is a whole number.
| 243 | |
| 17) | 4131 |
| 0 | |
| 41 | |
| 34 | |
| 73 | |
| 68 | |
| 51 | |
| 51 | |
| 0 |
17: Divisor
4131: Dividend
243: Quotient
0: Remainder
Now, as there are two digits after the decimal, the quotient will also have two digits after the decimal.
| 2.43 | |
| 17) | 41.31 |
If the divisor is not a whole number, then we have to move the decimal point over to as many places as it takes, to make it a whole number. The same has to be done with the dividend. If the dividend is also a decimal number, then move the decimal point over to as many places as you did in case of the divisor. Add some extra zeros to the dividend, if you have to. If the dividend is not a decimal number, then just append zeros to it, the number of which should be equal to the number of places that you have shifted the decimal in the divisor. Let’s understand this with an example:
Let’s say, we have solve 4.25/0.125 to find its quotient. Follow these steps for solving the sum:
- Step 1: To convert 0.125 to a whole number, you have to shift the decimal point to over three digits to the right. Then you get the whole number 125 as the divisor.
- Step 2: Now, move the decimal point in the dividend, 3 places to the right. But there are only 2 digits to the right of the decimal in this case. Hence, you will have you add a zero to the end of the dividend, and then shift the decimal 3 digits to the right. Hence, the dividend now becomes 4250. The division that you have to solve is now 4250/125.
- Step 3: Now, carry out the division as you normally would. The answer is 34.
Let us get our concepts cleared by taking a look at a few examples.
Here you don’t have a whole number to carry out the division directly. So, the first step will be to convert the numbers to whole numbers by shifting the decimal point. Always keep in mind to make the divisor a whole number. For example, if you have one digit after the decimal point in the dividend, shift the decimal point so that you get a whole number.
Here we can make the divisor 0.7 a whole number by shifting the decimal point by one place.
| 3.5 | ➜ | 35 |
| 0.7 | ➜ | 7 |
Now, we need to divide 35 by 7 by the usual long division method.
| 5 | |
| 7) | 35 |
| 0 | |
| 35 | |
| 35 | |
| 0 |
7: Divisor
35: Dividend
5: Quotient
0: Remainder
Since you have moved the decimal points of both the numbers, you don’t have to add a decimal point in your quotient. 35/7 is same as 3.5/0.7.
Here the dividend has two digits after the decimal point, whereas the divisor has only one digit after the decimal point. So, we will shift the decimal point in both the numbers by one digit.
| 9.69 | ➜ | 96.9 |
| 0.3 | ➜ | 3 |
Now we need to carry out the division of 96.9 by 3, which is an example of dividing decimal numbers by a whole number. As seen in the previous section, we will ignore the decimal point from 96.9.
| 323 | |
| 3) | 969 |
| 9 | |
| 06 | |
| 6 | |
| 09 | |
| 9 | |
| 0 |
3: Divisor
969: Dividend
323: Quotient
0: Remainder
Now as there is one digit after the decimal, the quotient will also have one digit after the decimal.
| 32.3 | |
| 3) | 96.9 |
Here the dividend has three digits after the decimal point, whereas the divisor has only two digits after the decimal point. So, we will shift the decimal point in both the numbers by two digits.
| 4.464 | ➜ | 446.4 |
| 0.08 | ➜ | 8 |
Now we need to carry out the division of 446.4 by 8, which is an example of dividing decimal numbers by a whole number. As seen in the previous section, we will ignore the decimal point from 446.4 and treat it as 4464.
| 554 | |
| 8) | 4464 |
| 0 | |
| 44 | |
| 40 | |
| 46 | |
| 40 | |
| 64 | |
| 64 | |
| 0 |
8: Divisor
4464: Dividend
558: Quotient
0: Remainder
Now, as there is one digit after the decimal, the quotient will also have one digit after the decimal.
| 55.8 | |
| 8) | 446.4 |
Here the dividend has three digits after the decimal point, whereas the divisor has only one digit after the decimal point. So, we will shift the decimal point in both the numbers by one digit.
| 3.888 | ➜ | 38.88 |
| 7.2 | ➜ | 72 |
Now, we need to carry out the division of 38.88 by 72, which is an example of dividing decimal numbers by a whole number. As seen in the previous section, we will ignore the decimal point from 38.88 and treat it as 3888.
| 54 | |
| 72) | 3888 |
| 0 | |
| 388 | |
| 360 | |
| 288 | |
| 288 | |
| 0 |
72: Divisor
3888: Dividend
54: Quotient
0: Remainder
Now as there are two digits after the decimal, the quotient will also have two digits after the decimal.
| 0.54 | |
| 72) | 38.88 |
Here the dividend has four digits after the decimal point, whereas the divisor has only two digits after the decimal point. So, we will shift the decimal point in both the numbers by two digits.
| 0.0098 | ➜ | 0.98 |
| 0.28 | ➜ | 28 |
Now, we need to carry out the division of 0.98 by 28, which is an example of dividing decimal numbers by a whole number. As seen in the previous section, we will ignore the decimal point from 0.98 and treat it as 98.
| 3.5 | |
| 28) | 98 |
| 0 | |
| 98 | |
| 84 | |
| 140 | |
| 140 | |
| 0 |
28: Divisor
98: Dividend
3.5: Quotient
0: Remainder
In the third step, we got the remainder as 14, which is smaller than the divisor, and hence, it cannot be divided by 28. So, we added an extra zero to it to make it dividable by 28. Here the quotient already has a decimal point. Now, as there are two digits after the decimal in the original dividend (0.98), the decimal point should be after two digits. We will shift the decimal point of 3.5 by two digits and make it 0.035.
| 0.035 | |
| 28) | 0.98 |
If you want to be able to do divisions involving decimals like a pro, then there is just one way to it―practice, practice, and practice. All the best!