# Long division with decimals in the dividend

In the division $\dfrac{8}{15}$ , what do we call the number 15?

## Long division with decimals in the dividend

Now, let’s look at how to use the long division method when the dividend is a decimal number. Let’s start with 73.52 divided by 2. As usual, draw a horizontal line. Write the two from the divisor below the line, just off to the left. Draw a small vertical line, then write the dividend.

Now, we will calculate from the left in the dividend, starting with the seven. 2 fits into 7... three times. Write 3 in the quotient, above the line. And 2 times 3 is 6.

We subtract this 6 from 7... This leaves 1. Next, bring the three from the dividend down. We fuse 1 and 3 into 13. 2 fits into 13 six times.

Write a six after the three in the quotient. 2 times 6 is 12 and 13 minus 12 is 1. Now, we have divided the whole number. We have the decimals left. We place a decimal point in the quotient too, directly above the position of the decimal in the dividend.

Then, we continue calculating. Bring the five down from the dividend. One and five, 15. This should be divided by 2. 2 fits into 15 seven times.

Add 7 to the quotient at the top. 2 times 7 is 14, which we subtract from 15. This leaves 1. Bring the two down. One and two, this is 12.

Let’s keep calculating. 2 fits into 12 six times. Let’s write 6 in the quotient. 2 times 6 is 12, and 12 minus 12 is 0. There is no remainder, so we are done.

73.52 divided by 2 is 36.76. It can be somewhat difficult to keep track of all decimals, and it takes a lot of practice to feel at ease with it. So, let’s have a look at another example. 0.63 divided by three. First, as usual, draw a horizontal line.

Below the line, to the left, is the divisor, 3. And to the right, the dividend, 0.63. 3 fits into 0 zero times. We write a zero in the quotient. 3 times 0 is 0.

and 0 minus 0 is obviously 0. It is time to calculate with the decimals in the dividend. Let’s write a decimal point in the quotient above the line. Bring the six from the dividend down. 3 fits into 6 two times.

Write a 2 in the quotient. 3 times 2 is 6, and 6 minus 6 is 0. Bring the three from the dividend down. 3 fits into 3 exactly once. Write a 1 after the two in the quotient.

3 times 1 is 3, and 3 minus 3 is 0. Now, we are finished. 0.63 divided by 3 equals 0.21. When you divide decimal numbers with long division, it is especially important to keep track of where the decimal point ends up. If you are not sure about the position of the decimal point, you can check if your answer is reasonable.

You can do this in different ways. One way is to draw a number line. 0, 1, 2, 3 … The dividend, 0.63, is here, right? Approximately. Between 0 and 1, but a bit closer to 1.

The answer we just found, 0.21, is also between 0 and 1, but a lot closer to 0. About here. Now, we can compare them. Is the dividend about three times as big as the quotient? Yes, approximately.

The answer is reasonable. The decimal point is in the correct position.