Converting Fractions into Decimals and Percentages

Transcript

Converting Fractions to Decimals and Percentages

Hello and welcome to this video about converting fractions to decimals and percents! In this video we will explore:

How to visually convert fractions to decimals and percents and
How to numerically convert fractions to decimals and percents

Before we get started, let’s review a couple of key concepts that we will use to help the math make sense.

Consider the fraction 10/10. One way to think about fractions is to think of them as division. 10 divided by 10 equals 1. In other words, ten tenths is one whole.

10/10 can be written equivalently as 100/100. The fraction bar can be said as “per”, so this expression can be said as “100 per 100”. The word “percent” literally means “per 100”, so “100 per 100” means 100 percent.

Therefore, when the same number is divided by itself, the result as a decimal is 1 and as a percent is 100%.

But what happens when our fraction is less than 1? Let’s take a look:

Consider the fraction ¼. Visually, this is what’s happening:

We can see in the diagram that 1/4 of the whole is \(\frac{25}{100}\). \(\frac{25}{100}\) means “25 per 100”, so it equals 25%.

Now let’s figure out how to convert this into a decimal.

First, we are going to take our fraction and reverse it. Instead of ¼, it is now 4/1, which is the same as saying 1 divided by 4.. Dividing this way doesn’t look like it will work. But using our knowledge of place value, we can make it work:

First, rewrite the 1 as 1.0. Instead of 1, the dividend is now ten tenths.
Second, 4 ones will go into ten tenths two tenths times (4 x .2 = .8).
Third, 4 x .2 = .8.

Fourth, 1.0 -.8 = .2
Fifth, rewrite the original dividend as 100 hundredths and bring the new 0 down.
Sixth, 4 ones goes into 20 hundredths 5 hundredths times (4 x .05 = .2).
Seventh, multiply 4 x .05 to get .20, and subtract to get 0.

This means ¼ = 0.25.

Let’s see this work with a non-unit fraction, like 3/16.

Here’s what the division looks like. The sequence of adding a decimal and dividing repeats as often as necessary until either the remainder is 0 or the decimal begins to repeat.

So, \(\frac{3}{16}=.1875. .1875=\frac{1875}{10000}=\frac{18.75}{100}\). Therefore, .1875 is the same as 18.75 per 100, so .1875 is 18.75%.

How about a repeating decimal? Everything is the same and the process can be stopped when it is clear the decimal repeats. Here’s a quick example – 1/3:

The process of subtracting 9 units from 10 units repeats, causing the decimal to repeat.

Lastly, consider a fraction that is greater than 1, such as \(\frac{5}{2}\).

Visually, here’s what we have:

We can see that the shaded quantity is \(\frac{1}{2}+\frac{1}{2}+\frac{1}{2}+\frac{1}{2}+\frac{1}{2}=\frac{5}{2}\). Each 1/2 equals 50, so we can say equivalently \(\frac{250}{100}\), which, as a decimal, is 2.5 (meaning 2 and a half wholes, which is what the diagram shows). We can also equivalently say 250 per 100, or 250%.

And the same works for the division as well:

Thanks for watching and happy studying!