# 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:

$3 \div 12 = 0.25$

3. Multiply the result by $$100$$:

$0.25 \times 100 = 25$

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:

$82$

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

$82 \div 100 = 0.82$

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 $$100$$):

$0.05 \times 100 = 5$

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

$5\%$

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:

$24$

2. and 3. Then, divide by $$100$$ and reduce the fraction to its lowest terms:

$\frac{24}{100} = \frac{6}{25}$

#### Example 2:

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

Solution:

1. First, we drop the percent sign:

$37.5$

2. Dividing it by $$100$$, we have:

$\frac{37.5}{100}$

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:

$\frac{375}{1\text{,}000} = \frac{15}{40} = \frac{3}{8}$

### 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:

$30 \div 100 = 0.3$

2. Then, we multiply $$120$$ by $$0.3$$:

$120 \times 0.3 = 36$

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.