How do we divide when there are decimal points involved?
Well, it is easier to divide by a whole number . so multiply by 10 until it is!
But we must do the same thing to both numbers in the division.
Example: 15 divided by 0.2
When we multiply the 0.2 by 10 we get a whole number:
But we must also do it to the 15:
So 15 Г· 0.2 has become 150 Г· 2 (both numbers are 10 times larger):
And so the answer is:
15 Г· 0.2 = 75
The number we divide by is called the divisor.
To divide decimal numbers:
Multiply the divisor by as many 10’s as we need, until it is a whole number.
Remember to multiply the dividend by the same number of 10’s.
Multiplying by 10 is easy, we just shift one space over like this:
Example: Divide 6.4 by 0.4
Let us move one space for both:
move 1 | ||
6.4 | 64 | |
0.4 | 4 | |
move 1 |
6.40.4 is exactly the same as 644
as we did the move for both numbers.
Now we can calculate:
644 = 16
So the answer is:
6.40.4 = 16
Are there really 16 lots of 0.4 in 6.4? Let’s see:
For harder questions we may need to use Long Division:
Example: Divide 0.539 by 0.11
First we need to make the move twice to make 0.11 into a whole number:
move 2 spaces | ||||
0.539 | 5.39 | 53.9 | ||
0.11 | 1.1 | 11 | ||
move 2 spaces |
0.5390.11 is exactly the same as 53.911
But what about 53.9? It still has a decimal point.
Well, we can ignore the decimal point in the dividend so long as we remember to put it back later.
First we do the calculation without the decimal point:
Now put the decimal point in the answer directly above the decimal point in the dividend:
The answer is 4.9
Example: Divide 9.1 by 7
The divisor (7) is already a whole number, so no need for any moves.
Now, ignore the decimal point in the dividend and use Long Division:
Put the decimal point in the answer directly above the decimal point in the dividend:
The answer is 1.3
Animations
Have a look at these Decimal Division Animations for further help.
Lastly .
As a final check we can put our “common sense” hat on and think “is that the right size?”, because we don’t want to pay ten times too much for anything, nor do we want to get only one-tenth of what we need!
Does the idea of dividing decimals bring on confusion and dread? We get it, decimal subtraction and addition is easy enough. But when long division is added to the equation, things suddenly get more complicated.
We’re here to tell you that dividing decimals is a lengthy but totally manageable process, and with this guide, you’ll be able to divide decimals with ease. Let’s get started!
Dividing With Decimals: Where to Start
The goal of the decimal division process is to find the quotient that results from dividing a decimal dividend by a decimal divisor. Let’s explain what these terms mean using the following decimal division problem:
In this equation, 66.82 is the dividend (the value that’s being divided) and 3.1 is the divisor (the value that the dividend is being divided by.) The answer that you’ll get when you divide the dividend by the divisor is called the quotient.
How to Divide Decimals by Decimals
Now that we’ve defined the terms, let’s walk through each step of decimal division:
Step 1: Make a general estimate of what you think the quotient will be. This can be done by rounding both the dividend and divisor to the closest whole number:
Now that these values have been rounded, you can use mental math or a calculator to divide them:
We’ve now determined an approximate value of what the quotient should be. This will come in handy later.
Step 2: Move the decimal place of the divisor to the right until it’s a whole number. The decimal of the dividend has to move the same number of decimal places. (In this case, that’s one digit to the right.)
As you can see, we’ve moved the decimal one place to the right for both values.
Step 3: Now we can start the division process:
Since 31 cannot fit into the value of 6, we need to determine what value we can multiply 31 by to get to close to 65. Multiplying 31 by 2 equals 62, so let’s put a 2 above the 65 and subtract the difference:
That gives us 3. Now let’s bring the 8 down.
Multiply 31 by 1 and subtract this value from 38.
Now let’s bring down the 2. Multiply 31 by 2 and subtract this value from 72.
Let’s bring down a zero and multiple 31 by 3. Then, subtract this value from 100.
Bring down another 0. Then subtract 31 multiplied by 2 from 70.
The remaining amount should be 8. Since we are going to round to the second decimal, we can stop here. We’ll explain this in the next step.
Step 4: The decimal point in the quotient needs to be at the same place as the dividend.
Though the quotient has three decimal numbers, let’s round to the second place value:
Step 5: Let’s compare our quotient to the original estimate in step one to determine if this is a reasonable answer:
Since the difference between 22 and 21.23 is less than one, our answer is indeed reasonable.
Mastering Decimal Division
Once you learn our five-step long division process, you can become the master of decimal division. Mastering this will help you with many other decimal related problems like adding, subtracting, and multiplying decimals.
Calculator Use
Do long division with decimal numbers and see the work for the calculation step-by-step. Enter positive or negative decimal numbers for divisor and dividend and calculate a quotient answer.
How to Do Long Division with Decimals
- If the number you’re dividing by has a decimal, move the decimal point all the way to the right counting the number of places you’ve moved it to. Then move the decimal point in the number you’re dividing the same number of places to the right.
- Insert a decimal point in the quotient (answer) space, exactly above the decimal point in the number under the division bar.
- Divide until the remainder is zero, or until you have enough decimal places in your answer. You can also stop if the remainder repeats because this indicates that your answer is a repeating decimal.
Calculate Decimal Places for a Quotient Answer
How far do you want to calculate the decimal places for the answer? Here are some examples:
- 31 divided by 16 = 1.937500 calculating to 6 decimal places
- 31 divided by 16 = 1.937 calculating to 3 decimal places
- 22 divided by 15 = 1.466666666 calculating 9 decimal places
- 22 divided by 15 = 1.466666 calculating 6 decimal places
- 22 divided by 15 = 1.466 calculating to 3 decimal places
Note that this is not the same as rounding to a specific number of decimal places. For example, 22 divided by 15 = 1.466 when calculated to 3 decimal places because you stop once you reach the third decimal place. On the other hand, 22 divided by 15 = 1.467 when rounded to 3 decimal places. In order to round to the third decimal place you must calculate to at least the fourth decimal place so that you know how to round the third decimal place. See our Rounding Numbers Calculator for more information.
Also see our Long Division with Remainders to see the work for long division with remainders.
Parts of Division
For the division problem 471 divided by 32:
- 471 is the dividend
- 32 is the divisor
- 14.718 is the quotient calculated out to 3 decimal places
How to do Long Division with Decimals: Example
In this problem we divide 4.71 by 3.2 out to 3 decimal places in the quotient answer.