Percentages are everywhere — they’re used in surveys, sales tax, and even in predicting the chance of rainy days. But what is a percentage? How do you calculate percentages, and how do you convert percentages into decimals when the need arises? Let’s take a look.

What Is a Percentage?

Before we can learn to easily convert percentages, it’s worth breaking down exactly what a percentage is.
We can start by looking at the word “percent”. When we break down this word, it is “per cent”. The "cent" part might remind you of a century, which is 100 years. It might also remind you of one cent, and we know that there are 100 cents in a dollar. Both examples point to the number 100. Therefore, whenever you write a percentage, it really means “x per 100”. In other words, 40 percent would be 40 per 100. This can also be interpreted as something that happens 40 times out of 100 times.

Finding Percentages

Now let’s look at finding percentages — how do you easily calculate percentages or deal with them if they appear in equations?
Let's start with an example. If you need to find 10 percent of a number, since that means one tenth of the number, you can simply divide the number by 10.
Example: Find

\(10\)

percent of

\(50\)

.
Solution: Divide

\(50\)

by

\(10\)

, which is

\(5\)

. Therefore,

\(5\)

is

\(10\)

percent of

\(50\)

.
Let's try a more difficult example.
Example: Find

\(25\)

percent of

\(56\)

.
Solution: We know that

\(25\)

percent is the same as

\(\frac{25}{100}\)

, or

\(\frac{1}{4}\)

. This means we just need to divide

\(56\)

by

\(4\)

, which is

\(14\)

.

Converting Percentages to Decimals

Sometimes it is necessary to convert a percentage to a decimal. This is helpful if you come across percentages inside a math expression, such as

\(110\%+.12\)

. For the percentage term, simply move the decimal two places to the left, and you can simplify the problem.
Example: Simplify the expression

\(110\%+.12\)

Solution:

\(110\%+.12\)

becomes

\(1.10+.12\)

, which yields

\(1.22\)

What's Next

At Cymath, our pre-algebra problems and solutions are designed to help students become confident problem solvers. Need a full solution for percentage problem, use Cymath as a percentage calculator. Want to get more practice? Tackle some of our tougher practice problems. You can also upgrade to Cymath Plus and enjoy additional explanations and steps to make learning even more effective.