# Converting Fractions into Decimals and Percentages

## 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:

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 $$\frac{10}{10}$$. One way to think about fractions is to think of them as division.

$$\frac{10}{10}=1$$
.

In other words, ten-tenths is one whole.

$$\frac{10}{10}$$ can be written equivalently as $$\frac{100}{100}$$. 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 $$\frac{1}{4}$$. Visually, this is what’s happening:

We can see in the diagram that $$\frac{1}{4}$$ 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.

We’re going to take our fraction $$\frac{1}{4}$$, 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.

Third, $$4\times 0.2=0.8$$.

Fourth, $$1.0 -0.8 = 0.2$$.

Fifth, we’re gonna 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 gonna multiply $$4\times 0.05=0.20$$. Then we’ll subtract to get 0.

This means $$\frac{1}{4}=0.25$$.

Let’s see this work with a non-unit fraction, like $$\frac{3}{16}$$.

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, $$\frac{3}{16}=0.1875$$ and $$0.1875=\frac{1,875}{10,000}=\frac{18.75}{100}$$. Therefore, 0.1875 is the same as 18.75% 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: $$\frac{1}{3}$$.

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 $$\frac{1}{2}=50$$, so we can say equivalently $$\frac{250}{100}$$, which, as a decimal, is 2.5 (meaning $$2\frac{1}{2}$$ wholes, which 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!

## Practice Questions

Question #1:

What is $$\frac{42}{100}$$ as a percent?

42%

4.2%

0.42%

420%

The correct answer is 42%. Percent means “per 100,” so to turn a fraction into a percent, convert the denominator to 100 and the numerator is your percentage.

Question #2:

What is $$\frac{16}{100}$$ as a decimal?

16.00

0.016

0.16

1.6

The correct answer is 0.16. Since 16 is over 100, write the decimal so that 6 is in the hundredths place, which means 1 will be in the tenths place.

Question #3:

Which of the following is not a proper way to rewrite $$\frac{96}{1,000}$$?

0.096

96%

9.6%

0.09600

The correct answer is 96%. $$\frac{96}{1,000}$$ as a decimal is 0.096 and adding zeroes to the end of a decimal number doesn’t change its value, so 0.09600 is equivalent to 0.096. $$\frac{96}{1,000}$$ as a percentage is 9.6%. 96% as a fraction is $$\frac{96}{100}$$.

Question #4:

What is $$\frac{7}{20}$$ as a percent?

7%

20%

28%

35%

The correct answer is 35%. Percent means “per 100,” so to turn a fraction into a percent, convert the denominator to 100 and the numerator is your percentage. To convert $$\frac{7}{20}$$ to have a denominator of 100, multiply both the numerator and the denominator by 5, which gives you $$\frac{35}{100}$$. 35 is the numerator, so $$\frac{7}{20}=35%$$.

Question #5:

What is $$\frac{23}{125}$$ as a decimal?

0.23

1.25

1.86

0.184

The correct answer is 0.184. To convert a fraction to a decimal, first convert the fraction so it has a denominator of a multiple of 10. This can be done by multiplying $$\frac{23}{125}$$ by $$\frac{8}{8}$$. $$\frac{23}{125}\times\frac{8}{8}=\frac{184}{1,000}$$, and since 184 is over 1,000, place the 4 in the thousandths place of the decimal, which puts 8 in the hundredths place, and 1 in the tenths place, 0.184.