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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\mathrm{%}$$\frac{1}{2}$$0.5$
In conversation, we might say Ben ate $50\mathrm{%}$ of the pizza, or $\frac{1}{2}$ of the pizza, or $0.5$ 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 $15\mathrm{%}$ to a simplified fraction.
$\begin{array}{rlr}15\mathrm{%}& =\frac{15}{100}& \text{Write the percent as a fraction}\\ \\ \\ \\ & =\frac{15÷5}{100÷5}& \text{Divide the top and bottom by 5}\\ \\ \\ \\ & =\frac{3}{20}& \text{Simplify}\end{array}$
We figured out that $15\mathrm{%}$ is equivalent to $\frac{3}{20}$.
Problem 1A
Convert $44\mathrm{%}$ to a simplified fraction.

### Fractions to percents

Let's convert $\frac{3}{5}$ to a percent. The key here is to turn $\frac{3}{5}$ to a fraction with a denominator of $100$. To do this, we need to know what times $5$ gives us $100$:
$5×\phantom{\rule{0.167em}{0ex}}?=100$
The number is $100÷5=20$:
$5×20=100$
Now we're ready to convert $\frac{3}{5}$ to a percent:
$\begin{array}{rlr}\frac{3}{5}& =\frac{3×20}{5×20}& \text{Multiply to get a denominator of 100}\\ \\ \\ \\ & =\frac{60}{100}& \text{Simplify}\\ \\ \\ \\ & =60\mathrm{%}& \text{Write as a percent}\end{array}$
We figured out that $\frac{3}{5}$ is equivalent to $60\mathrm{%}$.
Problem 1B
Convert $\frac{12}{25}$ to a percent.
$\mathrm{%}$

## Converting between percents and decimals

### Percents to decimals

Let's convert $8\mathrm{%}$ to a decimal:
$\begin{array}{rlr}8\mathrm{%}& =\frac{8}{100}& \text{Write the percent as a fraction}\\ \\ \\ \\ & =0.08& \frac{8}{100}\text{is 8 hundredths}\end{array}$
We figured out that $8\mathrm{%}$ is equivalent to $0.08$.

### Practice:

Problem 2A
Convert $4\mathrm{%}$ to a decimal.

### Decimals to percents

Let's convert $0.05$ to a percent:
$\begin{array}{rlr}0.05& =\frac{5}{100}& \text{This is 5 hundredths}\\ \\ \\ \\ & =5\mathrm{%}& \text{Write as a percent}\end{array}$
We figured out that $0.05$ is equivalent to $5\mathrm{%}$.
Problem 2C
Convert $0.14$ to a percent.
$\mathrm{%}$

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
Convert $0.3$ to a percent.
$\mathrm{%}$

## Practice set:

Problem 3A
Convert $0.82$ to a percent.
$\mathrm{%}$