# Converting between percents, fractions, & decimals

CCSS Math: 6.RP.A.3c
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\%$$\dfrac{1}{2}$$0.5$
In conversation, we might say Ben ate $50\%$ of the pizza, or $\dfrac12$ 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 $15\%$ 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 $15\%$ is equivalent to $\dfrac3{20}$.
Convert $44\%$ to a simplified fraction.

\begin{aligned} 44\% &= \dfrac{{44}}{100} &\small{\gray{\text{Write the percent as a fraction}}} \\\\\\\\ &= \dfrac{44 \div 4}{100 \div 4} &\small{\gray{\text{Divide the top and bottom by 4}}}\\\\\\\\ &= \dfrac{11}{25} &\small{\gray{\text{Simplify}}} \end{aligned}

### Fractions to percents

Let's convert $\dfrac35$ to a percent. The key here is to turn $\dfrac35$ to a fraction with a denominator of $100$. To do this, we need to know what times $5$ gives us $100$:
$5 \times \,\blueD? = 100$
The number is $100 \div 5 = \blueD{20}$:
$5 \times \blueD{20} = 100$
Now we're ready to convert $\dfrac35$ 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 $\dfrac35$ is equivalent to $60\%$.
Convert $\dfrac{12}{25}$ to a percent.
$\%$

The key here is to turn $\dfrac{12}{25}$ to a fraction with a denominator of $100$. To do this, we need to know what times $25$ gives us $100$:
$25 \times \,\blueD? = 100$
The number is $100 \div 25 = \blueD{4}$:
$25 \times \blueD{4} = 100$
Now we're ready to convert $\dfrac{12}{25}$ to a percent:
\begin{aligned} \dfrac{12}{25} &= \dfrac{{12 \times \blueD{4}}}{25 \times \blueD{4}} &\small{\gray{\text{Multiply to get a denominator of 100}}} \\\\\\\\ &= \dfrac{48}{100} &\small{\gray{\text{Simplify}}}\\\\\\\\ &= 48\% &\small{\gray{\text{Write as a percent}}} \end{aligned}
We figured out that $\dfrac{12}{25}$ is equivalent to $48\%$.

## Converting between percents and decimals

### Percents to decimals

Let's convert $8\%$ 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 $8\%$ is equivalent to $0.08$.
Convert $4\%$ to a decimal.

\begin{aligned} 4\% &= \dfrac{{4}}{100} &\small{\gray{\text{Write the percent as a fraction}}} \\\\\\\\ &= 0.04 &\small{\gray{\dfrac{4}{100}\text{is 4 hundredths}}}\end{aligned}
Convert $70\%$ to a decimal.

\begin{aligned} 70\% &= \dfrac{{70}}{100} &\small{\gray{\text{Write the percent as a fraction}}} \\\\\\\\ &= 0.70 &\small{\gray{\dfrac{70}{100}\text{is 70 hundredths}}}\end{aligned}

### Decimals to percents

Let's convert $0.05$ 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 $0.05$ is equivalent to $5\%$.
Convert $0.14$ to a percent.
$\%$

\begin{aligned} 0.14 &= \dfrac{{14}}{100} &\small{\gray{\text{This is 14 hundredths}}} \\\\\\\\ &= 14\% &\small{\gray{\text{Write as a percent}}}\end{aligned}
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!
Convert $0.3$ to a percent.
$\%$

\begin{aligned} 0.3 &=\dfrac{{3}}{10} &\small{\gray{\text{This is 3 tenths}}} \\\\\\\\ &=\dfrac{{30}}{100} &\small{\gray{\text{This is 30 hundredths}}} \\\\\\\\ &= 30\% &\small{\gray{\text{Write as a percent}}}\end{aligned}
Convert $0.9$ to a percent.
$\%$

\begin{aligned} 0.9 &=\dfrac{{9}}{10} &\small{\gray{\text{This is 9 tenths}}} \\\\\\\\ &=\dfrac{{90}}{100} &\small{\gray{\text{This is 90 hundredths}}} \\\\\\\\ &= 90\% &\small{\gray{\text{Write as a percent}}}\end{aligned}

## Let's practice!

Convert $0.82$ to a percent.
$\%$

\begin{aligned} 0.82 &= \dfrac{{82}}{100} &\small{\gray{\text{This is 82 hundredths}}} \\\\\\\\ &= 82\% &\small{\gray{\text{Write as a percent}}}\end{aligned}
Convert $9\%$ to a decimal.

\begin{aligned} 9\% &= \dfrac{{9}}{100} &\small{\gray{\text{Write the percent as a fraction}}} \\\\\\\\ &= 0.09 &\small{\gray{\dfrac{9}{100}\text{is 9 hundredths}}}\end{aligned}
Convert $\dfrac{8}{10}$ to a percent.
$\%$

The key here is to turn $\dfrac{8}{10}$ to a fraction with a denominator of $100$. To do this, we need to know what times $10$ gives us $100$:
$10 \times \,\blueD? = 100$
The number is $100 \div 10 = \blueD{10}$:
$10 \times \blueD{10} = 100$
Now we're ready to convert $\dfrac{8}{10}$ to a percent:
\begin{aligned} \dfrac{8}{10} &= \dfrac{{8 \times \blueD{10}}}{10 \times \blueD{10}} &\small{\gray{\text{Multiply to get a denominator of 100}}} \\\\\\\\ &= \dfrac{80}{100} &\small{\gray{\text{Simplify}}}\\\\\\\\ &= 80\% &\small{\gray{\text{Write as a percent}}} \end{aligned}
We figured out that $\dfrac{8}{10}$ is equivalent to $80\%$.
Convert $34\%$ to a simplified fraction.

\begin{aligned} 34\% &= \dfrac{{34}}{100} &\small{\gray{\text{Write the percent as a fraction}}} \\\\\\\\ &= \dfrac{34 \div 2}{100 \div 2} &\small{\gray{\text{Divide the top and bottom by 2}}}\\\\\\\\ &= \dfrac{17}{50} &\small{\gray{\text{Simplify}}} \end{aligned}
Convert $0.4$ to a percent.
$\%$

\begin{aligned} 0.4 &=\dfrac{{4}}{10} &\small{\gray{\text{This is 4 tenths}}} \\\\\\\\ &=\dfrac{{40}}{100} &\small{\gray{\text{This is 40 hundredths}}} \\\\\\\\ &= 40\% &\small{\gray{\text{Write as a percent}}}\end{aligned}