# Introduction to Converting a Percentage to a Decimal

As per the definition of a percentage, the percentage of a number x, x% = $\frac{x}{100}$

To convert this percentage to a decimal, we write it as a fraction and there is 100 in the denominator. To replace 100, we shift the decimal point two places to the left to get the decimal.

Rules to convert a percentage to a decimal

• First, we write the percentage with a decimal point.

For example, 12% = 12.0%

• Then shift the decimal point two places to the left.

For example, 0.12%

• Then we drop the percentage sign.

For example, 0.12. So, 12% = 0.12

Formula

By definition of a per cent, for any whole number x, x% = $\frac{x}{100}$ = 0.0x For example: 5% = $\frac{5}{100}$ = 0.05

Convert the following percentage to a decimal

72%

### Solution

Step 1:

By definition of a per cent, for any whole number x, x% = $\frac{x}{100}$ = 0.0x

Step 2:

The decimal point is shifted two places to the left and the percent sign is dropped.

So, 72% = 72.0% = 0.72

Convert the following percentage to a decimal

256%

### Solution

Step 1:

By definition of a per cent, for any whole number x, x% = $\frac{x}{100}$ = 0.0x

Step 2:

The decimal point is shifted two places to the left and the percent sign is dropped.

So, 256% = 256.0% = 2.56

Convert the following percentage to a decimal

8%

### Solution

Step 1:

By definition of a per cent, for any whole number x, x% = $\frac{x}{100}$ = 0.0x

Step 2:

The decimal point is shifted two places to the left and the percent sign is dropped.

So, 8% = 8.0% = 0.08