Decimal Long Division With a Decimal Number, Step 2.Long division is already a multi-step process, and adding a decimal point into the mix can make it feel twice as complicated. Decimal division relies on the same core steps as standard long division. The only extra consideration is making sure the decimal point is properly aligned in our answer.
Today, our tutors work through both decimal division cases students may run into. One case divides a decimal by a whole number, and the other divides by a decimal itself. We'll build each case step by step, the same way we would with any long division problem.
Decimal division is the process of splitting a number that includes a decimal point into equal parts.
We're asking the same question we always ask when we divide. How many times does one number fit into another?
To answer that question, we rely on three parts that every division problem shares:
Dividend: the number we're splitting up
Divisor: the number we're dividing by
Quotient: the answer to the problem
In decimal division, one or more of these three parts includes a decimal point instead of a whole number. That distinction gives us two situations to prepare for:
The dividend has a decimal point, and the divisor is a whole number, like 7.5 ÷ 5
The divisor also has a decimal point, like 7.5 ÷ 0.5
These two situations call for two different approaches, and we'll walk through both. The first, where we divide a decimal by a whole number, is more straightforward, so we'll start there.
We divide a decimal by a whole number using the exact steps of long division. The only new part is deciding where the decimal point belongs in our answer.
Let's work through 8.4 ÷ 6 together and see how that plays out.
We write 8.4 as the dividend and 6 as the divisor, just as we would with any division problem.
The divisor, 6, goes outside the division bracket
The dividend, 8.4, goes inside it
A decimal point goes in the answer, directly above the decimal point in 8.4.
We lock that spot in place first, so the point never has to move again.
Now, we look at the first digit of the dividend, 8, since that's the digit sitting closest to the decimal point on the left.
6 fits into 8 once, because 1 × 6 = 6.
That means 1 goes above the 8.
We multiply 1 by the divisor, 6, and that tells us how much of 8 we've accounted for.
1 × 6 = 6
We write that 6 directly beneath the 8.
Then, we subtract 6 from 8 to find what's left over after the first round of dividing.
8 − 6 = 2
We write 2 below the line.
2 is not enough by itself for 6 to divide into again, so we bring down the next digit from the dividend to continue the process.
The 4 from the tenths place comes down next to the 2, and together they form 24.
Since 6 fits into 24 exactly 4 times because 4 × 6 = 24, we write 4 above the tenths place.
We pair 4, our newest quotient digit, with the divisor, 6.
4 × 6 = 24
We write 24 directly beneath the 24.
24 minus 24 tells us what's left over after this round.
24 − 24 = 0
We write 0 below the line.
No digits remain to bring down, and nothing is left over.
Our final answer reads 1.4.
We can check the answer by multiplying it back.
1.4 × 6 = 8.4
Everything checks out!
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We divide a decimal by a decimal by first turning the divisor into a whole number. This step puts the problem in a form we already know how to solve.
Let's try and solve 8.3 ÷ 0.4.
We write 8.3 as the dividend and 0.4 as the divisor.
For long division to work, we need our divisor to be a whole number.
0.4 is a decimal number, and we need to move its decimal point to the right somehow.
So how do we do that?
We do that by multiplying 0.4 by 10, which turns it into 4.
The dividend needs the same treatment. 10 times 8.3 gives us 83.
We look at the first digit of the dividend, 8. Let’s see.
4 fits into 8 exactly 2 times, because 4 × 2 = 8, so 2 goes above the 8.
We pair 2, our new quotient digit, with the divisor, 4.
2 × 4 = 8
Then, we write 8 directly beneath the 8 in the dividend.
8 minus 8 tells us what's left over after this round.
8 − 8 = 0
We write 0 below the line.
4 needs another digit to divide into, so we bring down the next digit from the dividend to continue the process.
The 3 comes down next to the 0, and together they form 3.
Since 4 is larger than 3, and 83 has run out of digits to bring down, we need to extend the number.
To keep dividing, we need to add a zero after it, turning 83 into 830.
The 0 comes down next to the 3, forming 30.
4 fits into 30 exactly 7 times, because 7 × 4 = 28.
Now we write 7 above 0.
Next, we multiply 7 and 4 to get 28.
7 × 4 = 28
And we write 28 directly beneath the 30.
Then, we subtract 28 from 30 to get 2.
30 − 28 = 2
Which leaves us with a remainder again. We write the leftover 2 below the line.
Since 2 is too small to divide by 4, we add another zero to the dividend to keep going. We bring that zero down next to the 2 to form 20.
That new zero comes down next to the 2, forming 20.
4 fits into 20 exactly 5 times, because 4 × 5 = 20.
So we place 5 in the quotient directly above the zero.
Next, we multiply 5 by 4 to get 20.
5 × 4 = 20
We write the product directly beneath the 20.
Finally, we subtract 20 from 20, which leaves us with 0.
20 − 20 = 0
We write 0 below the line.
Since we moved the decimal point in 0.4 one place to the right to make it 4, we do the same in the quotient.
The decimal point goes directly above its position in the dividend, between the 2 and the 7.
The division is complete. Nothing remains to bring down, and the remainder sits at 0. That gives us a quotient of 20.75.
To confirm, we multiply the quotient by the original divisor of 0.4, not the whole number we converted it to.
20.75 × 0.4 = 8.3
The result matches our original dividend, so 20.75 is the correct answer.
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Our tutors put together six problems to test what we covered today. Work through each one using the method that fits, and show every step along the way.
9.6 ÷ 4
14.4 ÷ 8
4.5 ÷ 1.5
7.2 ÷ 0.6
Check your answers at the bottom of the guide.
Mathnasium tutors work through decimal division step by step with students. Over time, that practice makes long division and decimal placement second nature.
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Here are the answers.
9.6 ÷ 4 = 2.4
14.4 ÷ 8 = 1.8
4.5 ÷ 1.5 = 3
First, make the divisor a whole number by multiplying both numbers by 10:
4.5 × 10 = 45
1.5 × 10 = 15
7.2 ÷ 0.6 = 12
We also need to convert the divisor here into a whole number.
7.2 × 10 = 72
0.6 × 10 = 6
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