Converting Percentages to Decimals and Fractions

Converting Percentages to Decimals and Fractions

Hi, welcome to this video on converting percentages to decimals and fractions. In this video, we’ll show you some easy and not-so-easy methods for converting percentages.

We use decimals in every part of our lives. You see decimals when dealing with money, measuring distance, measuring how much something weighs. There are decimals, literally, everywhere you look. But before we look at conversions, let’s do a quick recap on percentages.

A percent is any number that is a part of 100. The word percent literally means “per one hundred”.

For instance, 25% is \(\frac{25}{100}\), and 64% is \(\frac{64}{100}\). But how do you convert the percentage into a decimal? Well, there are actually two ways you can do it.

The first way is by using math.

We’ve already established that percent means “per one hundred.” Using 25, 25% is really just 25 per 100. If you divide 25 by 100, you get 0.25, which is a decimal.

But there’s a much easier way to convert to a decimal, and it’s something I like to call the math two-step. Just move the decimal in your percentage 2 places to the left.

Let’s use 25% as our example. Twenty-five (25) has two digits, the two (2) and the five (5).

Our decimal is after the five (5). Moving the decimal two places to the left gives us 0.25. As always remember to remove the percent sign when you’re done.

Simple, right? But what if your percent number is over 100%? Maybe you have 125% Well the same applies. Move the decimal point two places to the left. You would move past the 5 — the first point — and past the 2 — the second point — and end with 1.25.

Now that we’ve got that down, let’s look at converting percentages into fractions.

This conversion has a few more steps.

When you convert a percentage to a fraction, you first convert your percentage to a decimal, then divide that number by one (1). Let’s stay with 25. 25% becomes 0.25. Now we divide that by one (1).

\(\frac{0.25}{1}\)

Next, for every number after the decimal point, multiply by 10. Since there are two numbers after the decimal in our example, we multiply 10 twice. If there were four numbers after the decimal, we would multiply 10 four times. The multiplication factor is essential to remember. You’re not “adding” 10 after each decimal point. You’re multiplying. In this case, you’ll multiply 10 times 10 which equals 100. So you’ll multiply the top number and the bottom number by 100.

\(\frac{0.25}{1}x\frac{100}{100}=\frac{25}{100}\)

Now, you have to simplify the fraction. You do that by finding the highest number that divides the top and bottom number equally. In this case, the answer is:
25
Twenty-five is the highest number that equally divides both twenty-five and one hundred. Here’s how the equation looks.
\(\frac{25}{100}\div \frac{25}{25}=\frac{1}{4}\)

And there you have it. The answer is \(\frac{1}{4}\)

That’s our look at converting percentages to decimals and fractions, with a little simplification thrown in. By following this lesson, you should have a firm base for these calculations, which prove useful in many areas of our lives.

Thanks for watching and happy studying!

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by Mometrix Test Preparation | Last Updated: September 16, 2019