Dividing Decimals Steps Rules and Examples

Dividing Decimals: Steps, Rules & Examples

In this lesson, you'll review some division terminology. Then, you'll learn the steps for decimal division and see them carried out in a few examples. Afterward, you can test your knowledge with a brief quiz.

Division Terminology

It'll be handy to review the parts of a division problem. When we're doing a division problem, the number we're dividing is the dividend. The number we're dividing by is called the divisor and the number we get from a division problem is the quotient.

Steps for Dividing with Decimals

The problem of 8 divided by 4 was easy enough. We're dealing with two whole numbers, so we just separate 8 into 4 groups to end up with 2 in each group. But what if we have decimals in our division problem? A decimal is a fraction of a whole number written as a number with a decimal point. 0.25 is an example of a decimal number.

If we follow a few simple steps, we can treat a decimal division problem like any other division problem. Let's consider 50 divided by 0.25.

Step 1: Move the decimal point to the right of the divisor's last digit. Since our divisor is 0.25, we'll need to move the decimal point two places to the right to place it after the 5.

What we're really doing is turning 0.25 into 25.0, or just 25. Now we can use this divisor more easily.

Step 2: However many places you move the decimal point to the right in the divisor, you'll need to move it the same number of places to the right in the dividend. In this case, our dividend is 50, which is the same as 50.00. When we move the decimal point two places to the right, we end up with 5,000.

Step 3: Proceed with division using the new divisor and dividend. Now, instead of having 50 divided by 0.25, we have 5,000 divided by 25. This new division problem is more familiar because we're dividing by a whole number.

When we divide 5,000 by 25, we get 200. We've found our quotient. 50 divided by 0.25 equals 200.

Decimals in the Divisor and Dividend

This division method works even if both the divisor and the dividend are decimal numbers. Take, for example, 0.86 divided by 0.2. Let's follow our steps:

Step 1: Since the divisor is 0.2, move the decimal point one place to the right and place it after the 2.

Moving the decimal gives us the new divisor of 2.0, which is the same as just 2.

Step 3: The division problem is now 8.6 divided by 2. In this case, we still have a decimal number as our dividend. Continue with normal division, but wherever the decimal point is in the dividend, put it in the same place in the quotient.

In this case, 2 goes into 8 four times. After the 4, insert a decimal point because that's where the decimal point is in the dividend. Now, continue dividing. 2 goes into 6 three times.

That means that the quotient is 4.3.

Anytime the dividend is a decimal number, the quotient will also be a decimal number since we have to bring the dividend's decimal point up into the quotient.

Let's look at another example. Divide 1 by 0.25.

To make the divisor a whole number, we need to move the decimal point two places to the right. This means we'll need to do the same with the dividend.

We can now carry on with our division.

The quotient is 4.

More Decimal by Decimal Division

Find the quotient of 0.25 divided by 0.5.

Let's set up the problem.

Now, we'll move the decimal point one place to the right in the divisor to make it a whole number. This means we'll also move the decimal point one place to the right in the dividend.

Now we can continue with normal division. Keep in mind, though, that we'll have to bring the decimal point up into the quotient from where it is in the dividend.

The quotient is 0.5.

Lesson Summary

Let's review. The number we're dividing is the dividend. The number we're dividing by is the divisor. The answer we get from a division problem is the quotient. Decimal division depends mainly on the divisor. Make the divisor a whole number in order to complete the division, according to the following steps:

First, move the divisor's decimal point to the right as many places as necessary to place it after the last digit and make it a whole number.

Then, move the dividend's decimal point the same number of places to the right. We can add a decimal point and zeroes after a whole number if necessary. For example, the whole number 5 equals 5.0 or 5.00, etc.

Proceed with division using the new divisor and dividend. If the dividend is a decimal number, bring the decimal point up into the same position in the quotient. Remember to always move the decimal point the same number of places to the right in both the divisor and dividend.