Dividing decimals can seem like a daunting task. Something as small as a little decimal point can add so much confusion that it can be tough to know where to begin.
You may be surprised to know that dividing decimals is incredibly straightforward. As long as you know how to do long division, you’ll be able to answer any decimal division problem.
All you need to do is take one extra step before starting your division process, but what exactly is that step? That’s what we’ll explain in this article.
We’ll take you through how to divide decimals by whole numbers, or by other decimal numbers, with practical examples so you can apply them to other problems. Let’s dive in!
Dividing decimals is not too different from dividing whole numbers; you just have to address the decimal point first before you can continue dividing. Knowing this, there are a few simple rules you can follow to ensure you don’t get stuck.
- Move the decimal in the decimal numbers to create a whole number. This is especially relevant for the divisor – the number you’re dividing by. Also, make sure to move the decimal point in the dividend – the number that’s getting divided – by the same number of places.
- Ensure the decimal point in the quotient – the final answer – is in the same place as the decimal point in the dividend.
- Now you can begin to divide the problem as usual.
There you have it; these three simple steps will ensure you’re able to divide a problem with decimal points in both the dividend and divisor, as well as divide decimals with whole numbers. Let’s take a look at some practice questions to see these rules in action.
Dividing decimals by whole numbers
To divide a decimal number by a whole number is incredibly similar to normal division. In this case, the dividend is a decimal, and the divisor is a whole number. To answer such a decimal division problem, we can use the long division method. Since the divisor is already a whole number, we don't need to move the decimal point first; we can go straight into division. Let’s see it in practice.
Example 1 – 105.25 ÷ 25
Step 1: We can write the problem in its standard form and keep the decimal place in its correct spot by putting it exactly above the decimal point on the dividend. Then, we can move on to the actual division.
Step 2: We know that 25 multiplies at least four times into 105.25. Therefore, we can write the number 4 in the ones column in the quotient directly and 100 (25 × 4) below the dividend.
Step 3: The next step is to subtract 105.25 by 100, which gives us 5.25. We can write this below the 100.
Step 4: This step involves doing the same thing we did in step 2, except now with 5.25. 25 does not go into 5. Therefore we can see if 25 goes into 52, which it does. We know that 25 multiplies two times into 52, which means we can write 2 in the quotient after the decimal place, and put 50 (25 × 2) below 5.25. It’s important to put the 5 below the 5 and the 0 below the 2 as these were the numbers involved in the calculation.
Step 5: As we did in step 3, we can then subtract 52 by 50, which equals 2, and write this number below in the tenth column. We can also bring down the 5 to give us 25.
Step 6: 25 goes into 25 exactly once. This means we can add 1 in the hundredths column in the quotient (next to the 2) and add 25 below the 25.
Step 7: Subtract 25 from 25, which gives us 0. As there is no other digit to bring down, this shows that we have reached our final answer.
Therefore, 105.25 ÷ 25 = 4.21
Let’s take a look at another example, but one where the divisor is bigger than the dividend.
Example 2 – 30.08 ÷ 64
Step 1: Write the problem in its standard form, keeping the quotient’s decimal point in the same place as the decimal point on the dividend. Then, we can move on to the actual division.
Step 2: 64 does not go into 30. However, we can add the 0 from the .08 to see if 300 can be divided by 64. We can deduce that 64 will not multiply into 300 five times, but it will multiply into 300 four times. Therefore, we can write 4 in the tenth column of the quotient and 256 (64 × 4) below the dividend.
Step 3: We can subtract 256 from 300 to give us 44 and write this below, and then bring the 8 down to make 448.
Step 4: This step involves doing the same thing we did in step 2, except now with the value 448. Luckily for us, 64 goes into 448 exactly seven times. This means we can add the digit 7 in the hundredths column of the quotient and write 448 (64 x 7) below the 448.
Step 5: Subtract 448 from 448, which gives us 0. As there is no other digit to bring down, this shows that we have reached our final answer.
Therefore, 30.08 ÷ 64 = 0.47
As you can see, this division problem has fewer total steps than the first one. However, the exact steps to reach our final answer are the same – simply keep repeating steps 2-5 for any problem until you have reached the final answer.
Dividing decimals by decimals
Dividing decimals by another decimal will follow the same process, except we first need to convert the divisor into a whole number. As we mentioned earlier, to do this, simply move the decimal point until it creates a whole number. You need to move the decimal point of the dividend in the same number of places you move the decimal point for the divisor. Let’s take a look at this in practice.
Example 1 – 9.6 ÷ 0.3
Step 1: Move the decimal point in 0.3 across one place to create the whole number, 3. The same would have to be done for 9.6, which makes 96. These would be our values through which we can solve the division problem.
Step 2: Write the problem 96 ÷ 3 in its standard form, keeping the quotient decimal point in the same place as on the dividend. Then we can move on to the actual division.
Step 3: We know that 9 can be divided by 3 exactly three times. This means we can put the digit 3 in the tens column of the quotient and 9 (3 × 3) below the dividend.
Step 4: Subtract 9 from 9, which equals 0, and write this below. We can then bring the 6 down to give us 06.
Step 5: We know that 6 can be divided by 3 exactly two times. This means we can put the digit 2 in the ones column of the quotient and 6 (3 × 2) below the 6.
Step 6: Subtract 6 from 6, which gives us 0. As there is no other digit to bring down, this shows that we have reached our final answer.
Therefore, 9.6 ÷ 0.3 = 32
This was a reasonably straightforward problem. Let’s take a look at a more challenging example.
Example 2 – 0.684 ÷ 0.18
Step 1: Move the decimal point in 0.18 across two places to create the whole number 18. The same would have to be done for 0.684, which makes 68.4. These would be our values through which we can solve this problem
Step 2: Write 68.4 ÷ 18 in its standard form, keeping the quotient decimal point in the same place as on the dividend. Then we can move on to the actual division.
Step 3: We can deduce that 18 does not go into 68 four times, but it will go three times. This means that we can put the digit 3 in the ones column of the quotient and 54 (18 × 3) below the dividend.
Step 4: Subtract 68 by 54, which equals 14, and write this below. We can then bring down the 4 to create 144.
Step 5: Using our times tables, we can calculate that 18 goes into 144 exactly eight times. This means we can put 8 in the tenth column of the quotient and write 144 (18 × 8) below.
Step 6: Subtract 144 by 144 to create 0. As there is no other digit to bring down, this shows that we have reached our final answer.
Therefore, 0.684 ÷ 0.18 = 3.8
Final thoughts
Dividing decimals can seem intimidating at first. But as you can see, it’s essentially the same as doing a regular long division problem.
Simply remember to move the decimal point of the divisor to create a whole number, and move the decimal point of the dividend by the same amount. Once you’ve completed this step, continue using the long division method as usual, and you’ll be able to solve any decimal division problem.
