Long division is a method that helps us divide large numbers and it works for decimals too – we'll show you how!
Whether you’re just starting to learn about dividing with decimals or brushing up for a math exam, this guide has got you covered.
Read on to find clear definitions, easy-to-follow instructions, solved examples, and practice exercises to help you master long division with decimals.
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Before we go into the long division with decimals, let’s take a moment to refresh our memory on the key terms: decimal and long division.
A decimal is a number in the base-10 system that includes a decimal point, which separates the whole number part on the left from the fractional part on the right.
For example, in 3.75, the "3" represents the whole number, and ".75" represents the fractional part.
We can think of decimals as an efficient way to express numbers that aren't whole, such as parts of a dollar or portions of a measurement. In 3.75, the ".75" tells us that we have three-quarters (or 75 out of 100) of a whole.
Long division is a step-by-step method used to divide larger numbers by breaking the process into smaller, simpler steps. It has four key components:
Dividend: The number we are dividing
Divisor: The number we are dividing by
Quotient: The result of the division
Remainder: The leftover value when the division doesn’t result in a whole number
The number of steps in long division can vary depending on the numbers we’re dividing, but the basic ones for whole numbers are:
Divide: Starting from the left, determine how many times the divisor fits into part or all of the dividend.
Multiply: Multiply the divisor by the current quotient digit.
Subtract: Subtract the result from the current portion of the dividend.
Bring Down: Bring down the next digit of the dividend.
Repeat: Continue the process until there is nothing left to bring down.
We will approach long division with decimals in two parts.
We’ll start by dividing whole numbers by decimals.
Then we’ll see how to divide decimals by decimals.
Ready?
Let’s get started.
At Mathnasium, we like to learn new concepts with examples, walking through the steps together.
Let’s divide 326 by 0.4 to see how long division with decimals works.
Before we start the steps, we can write the dividend, 326, inside the division symbol and the divisor, 0.4, outside, to the left of the division symbol.
Notice that we add a decimal point after 326, making it 326.0. That’s because any whole number can be written as a decimal number with zeros for the fraction part.
Adding the decimal now helps us correctly place the decimal in the quotient later.
Now, let’s go through the steps!
Step 1: Make the Divisor a Whole Number
Before dividing by a decimal number, we change the divisor to a whole number.
Since 0.4 (the divisor) has one decimal place, move the decimal point one place to the right to change it to 4. This is the same as multiplying the divisor by 10.
Since we multiplied the divisor by 10, we must also multiply the dividend by 10, changing 326.0 to 3260.
Doing this will give us the same quotient as division with the original numbers.
Step 2: Divide
Check how many times 4 (the divisor) goes into the first digit of 3260 (the dividend).
Since 4 can’t go into 3, look at the first two digits: 32.
Now, ask: How many times does 4 go into 32? The answer is 8 because 4 × 8 = 32.
Write 8 above the 2 in 3260 (since we used 32 in our division). This is the first digit of our quotient.
Step 3: Multiply & Subtract
Find the product of 8 and 4.
8 × 4 = 32
Write the product below 32 in the dividend and subtract it from 32.
32 — 32 = 0
Write 0 below the 32 to show the result of the subtraction.
Step 4: Bring Down
Bring down the next digit of the dividend, 6, and write it next to the 0.
Step 5: Divide Again
Now, check how many times 4 (the divisor) goes into 6.
4 goes into 6 one time because 4 × 1 = 4.
Write 1 above the 6 in the dividend. Now, we have two digits of the quotient, 81.
Step 6: Multiply & Subtract Again
Find the product of 1 and 4.
1 × 4 = 4
Write the result (4) below 6, then subtract it from 6.
6 — 4 = 2
Write 2 below the 4 to show the result of the subtraction.
Step 7: Bring Down Again
Bring down the next digit of the dividend, 0, and place it next to the 2, making 20.
Step 8: Divide Again
Now, check how many times 4 (the divisor) goes into 20.
4 goes into 20 exactly 5 times because 4 × 5 = 20.
Write 5 above the 0 in the dividend.
Step 9: Multiply & Subtract Again
Find the product of 5 and 4.
5 × 4 = 20
Write the result (20) below 20, then subtract it from 20.
20 — 20 = 0
The division is now complete because there are no more digits left to bring down, and the remainder is 0.
So, the final result of multiplying 326 by 0.4 is 815.
And that’s how we divide a whole number by a decimal! By multiplying the divisor and dividend by the same number, we turn the problem into a simple long division task.
Now, let's see how to divide a decimal by another decimal using an example.
This time, we will divide 0.832 by 0.16.
Before starting the steps, we place 0.832 (the dividend) inside the division symbol and 0.16 (the divisor) outside, to the left.
Step 1: Make the Divisor a Whole Number
Before dividing by a decimal number, we'll turn the divisor into a whole number to make the next steps in the division easier.
Since 0.16 (the divisor) has two decimal places, we multiply the divisor by 100 to move the decimal point two places to the right. This will change it to 16.
Now that we multiplied the divisor by 100, we must also multiply the dividend by 100, changing 0.832 to 83.2. This makes sure our quotient is the same as the 0.832 ÷ 0.16.
Step 2: Divide
Check how many times 16 (the divisor) fits into the first digit of 83.2 (the dividend).
Since 16 doesn’t fit into 8, we consider the first two digits, 83.
Next, check how many times 16 fits into 83. It goes in 5 times because 16 × 5 = 80.
Write 5 above the division symbol as the first digit of the quotient.
Step 3: Multiply & Subtract
Find the product of 5 and 16.
5 × 16 = 80
Write 80 below 83, then subtract it from 83.
83 — 80 = 3
Write the result (3) below.
Step 4: Bring Down
Bring down the next digit of the dividend, 2, and place it next to 3, making 32.
Step 5: Divide
Check how many times 16 fits into 32.
The answer is 2 because 16 × 2 = 32.
Write 2 next to 5 as the second digit of the quotient.
Step 6: Multiply & Subtract
Find the product of 2 and 16.
2 × 16 = 32
Write the result (32) below 32, then subtract it from 32.
32 — 32 = 0
Write the result below.
Since there are no more digits to bring down and the remainder is 0, we can stop dividing.
Step 7: Place the Decimal Point
Since we moved the decimal point in 0.832 two places to the right to make it 83.2, we do the same in the quotient. Place the decimal point directly above its position in the dividend, between 5 and 2.
Let’s go through a few more examples to explore different scenarios in long division with decimals.
We’ll divide 375 ÷ 0.15 using long division.
Before we start dividing, we write 375 (the dividend) inside the division symbol and 0.15 (the divisor) outside, to the left.
Notice that we add a decimal point after 375 making 375.0. That’s because any whole number can be written as a decimal number with zeros for the fraction part.
Also, adding the decimal now helps us correctly place the decimal in the quotient later.
Step 1: Make the Divisor a Whole Number
Since 0.15 has two decimal places, multiplying it by 100 moves the decimal point two places to the right, turning it into 15.
To make sure the quotient is the same as 375 ÷ 0.15, multiply 375 (the dividend) by 100.
375 × 100 = 37,500
Our new divisor is 15, and the dividend is 37,500.
Since we have converted the problem into a whole number division, we’ll now present the remaining steps visually.
So the final result of dividing 375 by 0.15 is 2,500.
Now, let’s divide 0.312 ÷ 0.13.
As always, before starting the steps, we place 0.312 (the dividend) inside the division symbol and 0.13 (the divisor) outside, to the left.
Step 1: Make the Divisor a Whole Number
Since 0.13 (the divisor) has two decimal places, we multiply the divisor by 100 to move the decimal point two places to the right. This will change it to 13.
Now that we multiplied the divisor by 100, we must also multiply the dividend by 100, changing 0.312 to 31.2. This makes sure our quotient is the same as the 0.312 ÷ 0.13.
Step 2: Divide
Check how many times 13 goes into 3.
Since 13 can’t fit into 3, we look at the first two digits of the dividend.
How many times does 13 fit into 31? The answer is 2 because 2 × 13 = 26.
We write 2 as the first digit of our quotient, right above 1 in the dividend.
Step 3: Multiply & Subtract
Find the product of 2 and 13.
2 × 13 = 26
Write 26 below 31, then subtract it from 31.
31 — 26 = 5
Write the result (5) below.
Step 4: Bring Down
Now, we bring down the next digit in the dividend, which is 2. We place it next to 5, making 52.
Step 5: Divide Again
Check how many times 13 goes into 52.
13 goes into 52 exactly 4 times because 13 × 4 = 52.
We write 4 as the second digit of the quotient, to the right of 2.
Step 6: Multiply & Subtract
Find the product of 4 and 13.
4 × 13 = 52
Write the result (52) below 52, then subtract it from 52.
52 — 52 = 0
Write the result (0) below.
Since there are no more digits to bring down and the remainder is 0, we stop dividing.
Step 7: Place the Decimal Point
Since we moved the decimal point in 0.312 two places to the right to make it 31.2, we must do the same in the quotient. Place the decimal point directly above its position in the dividend, between 2 and 4.
This will make 2.4.
So the final answer of dividing 0.312 by 0.13 is 2.4.
You May Also Like: Guide to Long Division with Remainders →
Over to you! Try these exercises on your own to practice long division with decimals and build your confidence.
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