# How Do You Calculate and Convert a Percentage?

A **percentage** is a proportion that shows a number as a part of a whole, with the “whole” always being \(100\). It can also be thought of as the numerator of a fraction with the denominator always equal to \(100\). The term “percentage” is derived from the Latin word “per centum”, which translates to “per hundred”. The symbol for percentage is \(\bf{\%}\). For example, if it rained \(34\) days in the last \(100\) days, we say that it rained \(34\%\) of the time.

## Calculating Percentage

You can use the following **steps** to calculate a percentage:

**1.** Determine the whole amount.

**2.** Divide the number you want to express as a percentage by the total.

**3.** Multiply the result by \(100\).

#### Example:

Suppose Joseph has three yellow pencils out of a total of \(12\) pencils. What percentage of his pencils are yellow?

**1.** The whole (total) amount is \(12\).

**2.** Divide the number of yellow pencils by the total number of pencils Joseph has:

**3.** Multiply the result by \(100\):

Adding a \(\%\) symbol, the answer is \(25\%\). So, \(25\%\) of Joseph’s pencils are yellow.

You can convert percentages to decimals or fractions and vice versa. Let’s look at all the conversion methods.

## Conversions Using Percentages

Sometimes it is necessary to convert percentages to other numeric representations and vice versa. Here are the basics for doing these conversions.

### Converting a Percentage to a Decimal

If we are given a percentage, it is very easy to convert it to a decimal:

**1.** Drop off the percentage sign (\(\%\)).

**2.** Move the decimal point two places left (this is the same as dividing by \(100\)).

#### Example:

What is \(82\%\) expressed as a decimal?

*Solution:*

**1.** First, we drop the percentage symbol:

**2.** Then, we simply move the decimal point two places left (i.e., divide by \(100\)):

*Note:* If a decimal point is not shown explicitly, always assume a number has a decimal at the end of it (on the right side).

### Converting a Decimal to a Percent

This is exactly the **reverse process of converting a percent to a decimal**:

**1.** Move the decimal point two places to the right (multiply by \(100\)).

**2.** Place a percentage sign (\(\%\)) at the end of the number.

#### Example:

What is \(0.07\) expressed as a percentage?

*Solution:*

**1.** First, we move the decimal point two places to the right (i.e., multiply the decimal by \(100\)):

**2.** Then, we simply place a percentage symbol at the end:

So, \(0.07\) expressed as a percentage is \(7\%\).

### Converting a Percent to a Fraction

We will look at two examples below to clarify how a percent is converted to a fraction. First, the **steps**:

**1.** Drop the percentage symbol.

**2.** Divide the number by \(100\). If the number is a decimal, move the decimal point until it becomes a whole number. Move the decimal point of the denominator the same number of places as you move the decimal point of the numerator.

**3.** Reduce, if possible.

#### Example 1:

What is \(24%\) expressed as a fraction and reduced to its lowest terms?

*Solution:*

**1.** First, we drop the percent sign:

**2.** and **3.** Then, divide by \(100\) and reduce the fraction to its lowest terms:

#### Example 2:

What is \(37.5\%\) expressed as a fraction and reduced to its lowest terms?

*Solution:*

**1.** First, we drop the percent sign:

**2.** Dividing it by \(100\), we have:

Since the numerator is a decimal, we multiply \(37.5\) by \(10\) to make it into a whole number. We multiply the denominator by \(10\) as well:

\[\frac{37.5 \times 10}{100 \times 10} = \frac{375}{1\text{,}000}\]**3.** Now, we just need to reduce this fraction to get the final answer:

### Converting a Fraction to a Percent

The best way to convert a fraction to a percentage is to **convert the fraction to a decimal first**, then follow the steps of decimal-to-percentage conversion. An example will shed some light on this process.

#### Example:

What is \(\frac{4}{5}\) expressed as a percentage?

*Solution:*

Dividing \(4\) by \(5\), we have:

\[4 \div 5 = 0.8\]We have changed the fraction to a decimal and now we follow the steps learned before for converting a decimal to a percentage:

\[0.8 \times 100 = 80\]That is \(80\%\).

### More Practice

Now that you have all the conversions ingrained in your brain, let’s look at a couple of examples: finding a certain percentage of a number and finding a number is what percent of another number.

#### Example 1:

Calculate \(30\%\) of \(120\).

*Solution:*

**1.** First, let’s convert the percentage to a decimal:

**2.** Then, we multiply \(120\) by \(0.3\):

Thus, \(30\%\) of \(120\) is \(36\).

*Note:* As the first step, we could have converted the percentage to a fraction instead of a decimal.

#### Example 2:

\(36\) is what percent of \(90\)?

*Solution:*

If we are given a problem in the form “\(n\) is what percent of \(m\)”, we always divide \(n\) by \(m\) and convert the result to a percentage, like so:

\[36 \div 90 = 0.4\] \[0.4 \times 100 = 40\] \[40\%\]*Note:* When dividing \(36\) by \(90\), we ended up with a decimal. Reducing the fraction \(\frac{36}{90}\) to its lowest terms and then converting it to a percentage is also another correct process.

For additional help with percentages and other math concepts, or to test your knowledge, check out our math practice tests, study guides, and flashcards.

## Keep Reading

Math Basics Blog

### The Greater Than Sign vs The Less Than Sign: How to Remember the Difference

Math symbols are not just a collection of squiggles on a page. Each one…

Math Basics Blog

### Understanding Function Notation

Functions are introduced as math studies get more abstract. The functio…

Math Basics Blog

### Help with Math Basics

Are numbers and calculations just among your strong suits? Do you cring…