# Fraction to Percent

To convert a fraction to a percent, we first convert it to decimal, multiply it by 100 to get the percentage value, and finally add a ‘%’ sign.

It helps us to compare and order two quantities more easily.

Let us convert ${\dfrac{1}{4}}$ to percent.

Dividing the Numerator by the Denominator of the Fraction

${\dfrac{1}{4}}$ = 0.25

Multiplying the Result by 100 and Moving the Decimal Point to the Right

0.25 × 100 = 25%

Here, the answer is less than 100% as  ${\dfrac{1}{4}}$ is a proper fraction.

## Formula

Thus, the formula to convert fraction ${\dfrac{p}{q}}$ to percentage is:

${\dfrac{p}{q}}$ = ${\left( \dfrac{p}{q}\times 100\right)}$ %

Here,

p = Numerator

q = Denominator

This is another way of converting a fraction to a percent where we multiply the fraction by 100, simplify it, and then add a ‘%’ sign.

For example,

${\dfrac{1}{4}}$ = ${\dfrac{1}{4}\times 100}$ = 25%

## Alternative Method

In this method,  we find the equivalent fraction with a denominator of 100. Then, the numerator with the ‘%’ sign represents the percent.

Let us convert ${\dfrac{1}{4}}$ into percent.

Multiplying the Denominator by a Number to get 100

Since 4 × 25 = 100

Thus, we multiply 25 by the denominator 4 to get 100

Multiplying the Numerator by the Same Number

${\dfrac{1\times 25}{4\times 25}}$ = ${\dfrac{25}{100}}$

Writing the Numerator with the ‘%’ Sign

Thus, the percentage is 25%

## Fraction to Percent Table

Here is a fractions-to-percent conversion table for your use.

## For Improper Fractions

While converting an improper fraction to a percent, we follow the same steps.

Let us convert ${\dfrac{9}{4}}$ to percent.

Converting to Decimal Number

${\dfrac{9}{4}}$ = 2.25

Multiplying the Decimal Number by 100

2.25 × 100 = 225%

Here, we observe that the answer is above 100%, as ${\dfrac{9}{4}}$ is an improper fraction.

## Solved Examples

What is ${\dfrac{13}{20}}$ in percent form?

Solution:

Here, ${\dfrac{13}{20}\times 100}$ = 65%

What is ${\dfrac{2}{5}}$ as a percent?

Solution:

Here, ${\dfrac{2}{5}\times 100}$ = 40%

E.g.3.

What is ${\dfrac{12}{20}}$ as a percent?

Solution:

Here, ${\dfrac{12}{20}\times 100}$ = 60%

E.g.4.

Compare the fractions ${\dfrac{3}{4}}$ and ${\dfrac{16}{20}}$ by converting them to percentages.

Solution:

Here, ${\dfrac{3}{4}\times 100}$ = 75%
${\dfrac{16}{20}\times 100}$ = 80%
Since 80% > 75%
Thus, ${\dfrac{16}{20}}$ > ${\dfrac{3}{4}}$