Convert Percentage into Decimal

Converting a percentage into a decimal is an essential skill in mathematics that helps in various calculations, including financial analysis, statistics, and everyday math.

Here’s a detailed explanation:

Understanding Percentages and Decimals

Percentage: A percentage represents a part per hundred. For example, 50% means 50 out of 100.

Decimal: A decimal is another way to represent fractions and percentages.

It uses a base of 10 to show parts of a whole.

Steps to Convert Percentages to Decimals

1. Remove the Percent Sign:

The first step is to simply get rid of the percent sign (%). This isolates the numerical value of the percentage.

2. Divide by 100:

After removing the percent sign, divide the numerical value by 100.

This conversion is based on the fact that “percent” literally means “per hundred.

3. “Why Divide by 100?

Dividing by 100 effectively shifts the decimal point two places to the left, which converts the percentage to a fraction of one (a decimal).

Detailed Examples

Let’s break down the process with different examples:

Converting a percentage into a decimal is a simple process.

Here are the steps:

Remove the percent sign (%):

A percentage is a number followed by a percent sign, like 50%.

Divide by 100:

To convert the percentage to a decimal, divide the number by 100.

Here’s a step-by-step example:

Example:

Percentage: 50%

Step 1: Remove the percent sign: 50

Step 2: Divide by 100

50÷100

0.50

50÷100=0.50

So, 50% as a decimal is 0.50.

Another example

Percentage: 75%

Step 1: Remove the percent sign: 75

Step 2: Divide by 100:

75÷100

0.75

75÷100=0.75

So, 75% as a decimal is 0.75.

Quick Reference:

1% = 0.01
10% = 0.10
25% = 0.25
50% = 0.50
100% = 1.00

Shortcut:

To convert a percentage to a decimal, we can also move the decimal point two places to the left.

50% becomes 0.50
7.5% becomes 0.075
125% becomes 1.25

This method works because moving the decimal two places to the left is equivalent to dividing by 100.

Example 1: Converting 85%

Remove the percent sign: 85%

Divide by 100:

85÷100

0.85

85÷100=0.75

So, 85% as a decimal is 0.85.

Example 2: Converting 4%

Remove the percent sign: 4%

Divide by 100:

4÷100

0.04

4÷100=0.04

So, 4% as a decimal is 0.04.

Example 3: Converting 150%

Remove the percent sign: 150%

Divide by 100:

150÷100

150÷100=1.50

So, 150% as a decimal is 1.50.

Shortcut Method:

Moving the Decimal Point

Instead of dividing by 100, we can move the decimal point two places to the left.

This is a quick way to convert percentages to decimals.

Using the Shortcut:

75%: Move the decimal point two places left → 0.75

4%: Move the decimal point two places left → 0.04

150%: Move the decimal point two places left → 1.50

Practice Problems

Convert 20% to a decimal:

Remove the percent sign: 20

Divide by 100 or move the decimal:

20÷100

0.20

20÷100=0.20

Answer: 0.20

Convert 85% to a decimal:

Remove the percent sign: 85

Divide by 100 or move the decimal:

85÷100

0.85

85÷100=0.85

Answer: 0.85

Convert 7.5% to a decimal:

Remove the percent sign: 7.5

Divide by 100 or move the decimal:

7.5÷100

0.075

7.5÷100=0.075

Answer: 0.075

Summary

Remove the percent sign: Start by taking away the % symbol.
Divide by 100: This converts the number from a percentage to a decimal.
Shortcut: Move the decimal point two places to the left.
Understanding and practicing these steps will make converting percentages to decimals second nature.