# Fraction to percent

There are a number of ways to convert a fraction to a percent. Depending on what resources are available, it can be relatively simple or somewhat tedious, but in any case, it requires an understanding of what fractions, decimals, and percentages are.

## Fractions, percents, and decimals

Fractions and percents represent parts of a whole. While a fraction can be any ratio, percentages represent parts relative to a hundredth of a part. Thus, if a given fraction is, or can be written as an equivalent fraction such that the denominator is 100, then converting the fraction to a percent is trivial: the numerator is the percent.

If we were to perform the division problem to convert the fraction to a decimal, we would find that:

This gives us the relationship between decimals and percentages. To convert a decimal to a percentage, multiply by 100. This is equivalent to shifting the decimal place two places to the right. We don't need to actually perform the multiplication due to the nature of the decimal numeral system: each place represents a power of 10, and since 100 = 10^{2}, shifting the decimal point two places to the right is the same as multiplying by 100.

Knowing these relationships allows us to use a variety of strategies to convert fractions to percentages.

## Converting fractions to percents using decimals

Multiplying any decimal by 100 (shifting the decimal point to places to the right) will convert that decimal into a percent. As such, if a calculator is available, the simplest way to convert a fraction to a percent is to perform the division problem then multiply the result by 100 to obtain the percent.

If no calculator is available, use long division (or other methods) to convert the fraction into a decimal, then multiply the result by 100. This is a guaranteed way to convert a fraction to a percent, though depending on what the fraction is, the long-division can be tedious depending on what level of precision is necessary.

## Converting fractions to percents using equivalent fractions

The term percent comes from "per centum," which is latin for "by a hundred." It refers to the fact that percents are ratios that are expressed as a fraction of 100. As such, the percent form of any fraction of 100 is simply the numerator of the fraction. In some cases (such as with ¼), it may be relatively simple to convert the denominator of a given fraction to 100. In cases that are not as simple, we can use proportions and basic algebra to express a given fraction as an equivalent fraction of 100.

Example

Convert to a percent using equivalent fractions.

First, set up a proportion such that x is the %:

Solve for x by cross multiplying the fractions, then isolating x:

Therefore, , so is equal to 15.789%.