# Converting Between Percentages and Decimals

In this lesson, we convert between percentages and decimals. This means we solve problems involving converting both percentages into decimals and decimals into percentages as well. This involves shifting the decimal point two places either to the left or to the right and then dropping or adding the percent sign.

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

Rules to convert a decimal to a percentage

• First, we write the decimal.

For example, 0.43

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

For example, 43.0

• Then we add the percentage sign.

For example, 43.0% So, 0.43 = 43.0% = 43%

We have put a 0 as a place holder as we are one digit short.

Solving the problem

Writing/Converting 0.276 as a percentage

0.276 = 27.6%

Here we have moved the decimal point two places to the right to convert to a percentage.

Write 4.5% as a decimal

### Solution

Step 1:

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

Step 2:

To convert the percentage to a decimal, the decimal point is shifted two places to the left and we have put a 0 as a place holder as we are one digit short. Then the percent sign is dropped.

So, 4.5% = 0.045

Write 0.378 as a percentage

### Solution

Step 1:

To convert a decimal to a percentage we multiply it by 100. It is same as shifting the decimal 2 places to the right and adding a percent sign.

Step 2:

So, 0.378 = 37.8%

Write 127% as a decimal

### Solution

Step 1:

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

Step 2:

To convert the percentage to a decimal, the decimal point is shifted two places to the left and we have put a 0 as a place holder as we are one digit short. Then the percent sign is dropped.

So, 127% = 127.0% = 1.27