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 over 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 over 10 can also be equivalently written as 100 over 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 1 over 4.
Visually, this is what’s happening:
We can see in the diagram that one-fourth of the whole is 25 over 100.
25 over 100 means “25 per 100”, so it equals 25 percent.
Now let’s figure out how to convert this into a decimal.
We're going to take our fraction, one-fourth, 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 10 tenths, 2 tenths times.
Third, 4 times 2 tenths is equal to 8 tenths.
Fourth, 1 minus 8 tenths is equal to 2 tenths.
Fifth, we're going to rewrite the original dividend as 100 hundredths and bring the new 0 down.
Sixth, 4 ones goes into 20 hundredths, 5 hundredths times.
Seventh, we're going to multiply 4 times 5 hundredths to get 20 hundredths.
Then we'll subtract to get 0.
This means that one-fourth is equal to 25 hundredths.
Let’s see this work with a non-unit fraction, like 3 over 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, 3 over 16 is equal to 0.1875.
And 0.1875 is equal to 1,875 over 10,000.
And this is equal to 18.75 over 100.
Therefore, 0.1875 is equal to 18.75 percent because it's 18.75 per 100.
How about a repeating decimal?
Everything is the same and the process can be stopped when it is clear that the decimal repeats.
Here’s a quick example, 1 over 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 5 over 2.
Visually, here’s what we have:
We can see that the shaded quantity is one-half plus one-half, plus one-half, plus one-half, plus one-half,
which is equal to 5 halves.
Each half equals 50, so we can say equivalently 250 over 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 percent.
And the same works for the division as well:
Thanks for watching and happy studying!