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Writing Percents in Decimal and Fraction Form

Percentage is nothing but a fraction with 100 as it's denominator. This means that 50% is equivalent to $\frac{50}{100}$ which is ½. This concept is used along with the understanding that fractions mean division, to convert percentage, decimals and fractions from one form to another.

This means we can convert percentage to decimal and vice versa and also from from percentage to fraction and vice versa.

Conversion from Percentage to Decimal Form

It is very easy to convert a percent to decimal. All you have to do is to move the decimal point by two places to the left.This is nothing but dividing the number by 100.

The following math homework example gives a step by step solution.

Example: 34% = 0.34

75% = 0.75

What is 100% in decimal form? It is 1!

Steps to convert from Percentage to Decimal Form:

Step 1: Divide the number by 100.

Step 2: Remove the % symbol.

Conversion from Percentage to Fraction Form

To convert from percent to fraction,

consider 75%

Step 1: Write the percent in the form a fraction with denominator as 100.

75% = $\frac{75}{100}$

Step 2: Write this fraction in its lowest form(Reduce the fraction)

$\frac{75}{100}$ = ¾

Hence, 75% = ¾.

Steps to be followed to convert from Percentage to Fraction Form.

Step 1: Eliminate the % symbol.

Step 2: Write the fraction with the number in the place of numerator and 100 in the place of denominator.

Step 3: Reduce the fraction to the simplest form as the need be.

Conversion from Decimal to Percent

Consider 0.12, it can be written in percent form by moving the decimal point to the right by two places and then add a percent sign(%).

0.12 = 12%

0.002 = 0.2 %

Steps to convert from Decimal to Percent Form

Step 1: Simply multiply the given decimal by 100.

Step 2: Add a % symbol at the end of the product obtained.

Conversion of Fractions to Percent

There are two ways to do this

Method 1:

  1. Start by converting the fraction to decimal

  2. then move the decimal to the right by 2 decimal places

  3. Add a percent sign(%)

Example: Convert $\frac{3}{8}$ to percent form.

Solution: 3 ÷ 8 = 0.375

0.375 = 37.5 %

Therefore, $\frac{3}{8}$ = 37.5%

Method 2:

  1. Multiply and divide the given fraction by a number, so that the denominator will become 100.

  2. Now we just have to leave out the denominator and write the numerator with a percent sign.

Convert ¾ into Percentage

Solution:

We have to write a fraction that is equivalent to $\frac{3}{4}$ which has a denominator 100. By looking at the denominator, we know that 4 X 25 = 100 OR $\frac{100}{4}$ = 25

Hence multiply the numerator and denominator by 25

¾ X $\frac{25}{25}$ = $\frac{75}{100}$

Now leave out the denominator and write the numerator with a percent sign.

75%

Hence, ¾ = 75%

There are cases, when we get a recurring decimal or non-terminating decimals when we convert from fraction to decimal OR we may not be able to find an equivalent fraction with denominator of 100 of the given fraction.

Convert $frac{2}{3}$ to Percentage

Solution:

$\frac{2}{3}$ = 0.666666........

So it is a recurring decimal!

It can be rounded as 0.667.

hence, $\frac{2}{3}$ = 66.7%

OR

We can write 0.666666.... as 0.66 $\frac{2}{3}$

Hence, we get, 66 $\frac{2}{3}$ %

Steps to convert from Fractions to Percentage Form

Step 1: Divide the numerator of the given fraction by its denominator.

Step 2 : Round up the quotient to the required precision if needed.

Step 3: Now multiply the quotient obtained in the previous step by 100.

Step 4: Add a % symbol at the end of the number.