# How to Divide Numbers with Decimals

This is the fourth part and the conclusion of the Operations on Decimals series. In this post, we are going to discuss how to divide numbers with decimals.

In the examples below, it is assumed that you already know how to divide decimal numbers by whole numbers. Therefore, the basic idea is to eliminate the decimal point of the divisor. It can done by multiplying both the divisor and the dividend by powers of 10.

Example 1: What is 18.5 divided by 0.2?

To get rid of the decimal point in 0.2, we multiply it by 0. If we do this, we also multiply 8.5 by 10. This gives us 185 divided by 2 which 92.5.

Example 2: What is 4.26 divided by 0.3?

To get rid of the decimal point in 0.3, we multiply it with 10. We also multiply 4.26 by 10. This gives us 42.6 divided by 3. Well, we can actually do this mentally: 42 divided by 3 is 14 and 0.6 divided by 3 is 0.2. So, the correct answer is 14.2

Example 3: What is 32.85 divided by 0.203?

Well, just multiply 0.203 by 1000; this results to 203. Now, multiply 32.85 by 1000, this gives us 32850. So, the new given now is, 32850 divided by 203. Well, I’m sure you can do that.

Why does multiplying by powers of 10 works?

If you divide a by b, then you have the fraction $\displaystyle \frac{a}{b}$. Now, when we multiply the dividend and divisor with the same number, we are actually multiplying the numerator and denominator with that number. For instance, if we multiply $a$ and $b$ by 10, we have

$\displaystyle \frac{a \times 10}{b \times 10} = \frac{10a}{10b} = \frac{a}{b}$

we are not actually changing its value of the fraction. Therefore, we are still dividing the same numbers.

Now that concludes our series. In the next post, we will be discussing about percent.