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# Converting between percents, fractions, & decimals

For example, learn how 50%, 1/2, and 0.5 are all equivalent.
Percents, fractions, and decimals are all just different ways of writing numbers. For example, each of the following are equivalent:
PercentFractionDecimal
50, percentstart fraction, 1, divided by, 2, end fraction0, point, 5
In conversation, we might say Ben ate 50, percent of the pizza, or start fraction, 1, divided by, 2, end fraction of the pizza, or 0, point, 5 of the pizza. All three of these phrases mean the exact same thing.
In this article, we'll learn how to convert between percents, fractions, and decimals.

## Converting between percents and fractions

### Percents to fractions

Let's look at an example converting 15, percent to a simplified fraction.
\begin{aligned} 15\% &= \dfrac{{15}}{100} &\small{\gray{\text{Write the percent as a fraction}}} \\\\\\\\ &= \dfrac{15 \div 5}{100 \div 5} &\small{\gray{\text{Divide the top and bottom by 5}}}\\\\\\\\ &= \dfrac{3}{20} &\small{\gray{\text{Simplify}}} \end{aligned}
We figured out that 15, percent is equivalent to start fraction, 3, divided by, 20, end fraction.
Problem 1A
Convert 44, percent to a simplified fraction.

### Fractions to percents

Let's convert start fraction, 3, divided by, 5, end fraction to a percent. The key here is to turn start fraction, 3, divided by, 5, end fraction to a fraction with a denominator of 100. To do this, we need to know what times 5 gives us 100:
5, times, start color #11accd, question mark, end color #11accd, equals, 100
The number is 100, divided by, 5, equals, start color #11accd, 20, end color #11accd:
5, times, start color #11accd, 20, end color #11accd, equals, 100
Now we're ready to convert start fraction, 3, divided by, 5, end fraction to a percent:
\begin{aligned} \dfrac35 &= \dfrac{{3 \times \blueD{20}}}{5 \times \blueD{20}} &\small{\gray{\text{Multiply to get a denominator of 100}}} \\\\\\\\ &= \dfrac{60}{100} &\small{\gray{\text{Simplify}}}\\\\\\\\ &= 60\% &\small{\gray{\text{Write as a percent}}} \end{aligned}
We figured out that start fraction, 3, divided by, 5, end fraction is equivalent to 60, percent.
Problem 1B
Convert start fraction, 12, divided by, 25, end fraction to a percent.
percent

## Converting between percents and decimals

### Percents to decimals

Let's convert 8, percent to a decimal:
\begin{aligned} 8\% &= \dfrac{{8}}{100} &\small{\gray{\text{Write the percent as a fraction}}} \\\\\\\\ &= 0.08 &\small{\gray{\dfrac{8}{100}\text{is 8 hundredths}}}\end{aligned}
We figured out that 8, percent is equivalent to 0, point, 08.

### Practice:

Problem 2A
• Current
Convert 4, percent to a decimal.

### Decimals to percents

Let's convert 0, point, 05 to a percent:
\begin{aligned} 0.05 &= \dfrac{{5}}{100} &\small{\gray{\text{This is 5 hundredths}}} \\\\\\\\ &= 5\% &\small{\gray{\text{Write as a percent}}}\end{aligned}
We figured out that 0, point, 05 is equivalent to 5, percent.
Problem 2C
Convert 0, point, 14 to a percent.
percent

Converting from a decimal to a percent can be tricky when the decimal is in tenths. Let's see if you can figure it out!

### Practice:

Problem 2D
• Current
Convert 0, point, 3 to a percent.
percent

## Practice set:

Problem 3A
• Current
Convert 0, point, 82 to a percent.
percent