Percentage Formula: How to Calculate Percentage
Understanding how to calculate percentages is an essential skill that everyone should possess. Whether for calculating discounts during a sale or analyzing data in a statistical report, the ability to work with percentages is crucial. One of the easiest and most versatile ways to calculate percentages is using the percentage formula. In this article, we'll explore the percentage formula, how it works, and examples of how to use it in everyday situations.
Table of Content
What is the Percentage Formula?
Percentage is a way of expressing a number as a fraction of 100. It is often denoted with the symbol "%". It is useful in many fields, including finance, statistics, and science. The percentage formula is a simple mathematical equation that helps calculate a percentage based on two values - the part and the whole. The part is the value you're interested in, and the whole is the total value of the group or category.
The formula is expressed as:
Percentage = (Part / Whole) x 100
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Percentage Formula Example
Example 1: If you want to determine what percentage of the total sales revenue comes from a specific product, use the percentage formula.
The total sales revenue for the month was $50,000, and the sales revenue for the specific product was $10,000.
Solution
To find out what percentage of the total sales revenue comes from the specific product, you would use the formula as follows:
Percentage = (10,000 / 50,000) x 100
Percentage = 20%
So, the specific product accounts for 20% of the total sales revenue. This is just one example of how the percentage formula can be used in everyday situations.
Example 2: A survey was conducted with 500 participants, and 350 preferred online shopping over in-store shopping. What percentage of participants prefer online shopping?
Solution:
Since the total number of seats is 100, and 85 are occupied, 85% of the seats are occupied.
To find the percentage of participants who prefer online shopping:
Percentage = (350 / 500) × 100 = 70%
=> 70% of participants will prefer online shopping.
Practice Problem:
- If there are 100 seats in a theatre and 85 are occupied, what percentage of seats are occupied?
- If a student answers 75 questions correctly out of a total of 120 questions on a test, what percentage of the questions did they answer correctly?
Percentage Change in Two Numbers
Percentage change between two numbers is a way of expressing the difference between the two numbers as a percentage of the original number. It is often used to measure the changes in stock prices, sales figures, or economic indicators. Percentage change between two numbers can be categorized into two types: percentage increase and percentage decrease.
Calculating Percentage Increase
To calculate the percentage increase between two numbers, follow these steps:
- Subtract the original number from the new number.
- Divide the difference by the original number.
- Multiply the result by 100.
i.e.,
Percentage Increase = ((New Number - Original Number) / Original Number) * 100
Let's take an example to get a better understanding of the percentage increase formula.
Example:
What is the percentage increase in sales if a company's sales increase from $200,000 in one year to $250,000 the next year?
Solution:
- Difference: $250,000 - $200,000 = $50,000
- Divide by Original Number: $50,000 / $200,000 = 0.25
- Convert to Percentage: 0.25 × 100 = 25%
The sales increased by 25% from one year to the next.
Calculating Percentage Decrease
The process for calculating percentage decrease is similar to that for percentage increase but focuses on situations where the new number is less than the original number.
- To find the difference, subtract the new number (end value) from the original number (start value).
- Divide the difference by the original number.
- Multiply the result by 100 to convert it to a percentage.
The formula for calculating percentage decrease is:
Percentage Decrease = ((Original Number - New Number) / Original Number) * 100
Let's take an example to get a better understanding of the percentage increase formula.
Example:
If a city's population decreases from 50,000 to 45,000, what is the percentage decrease in population?
Solution:
- Difference: 50,000 - 45,000 = 5,000
- Divide by Original Number: 5,000 / 50,000 = 0.1
- Convert to Percentage: 0.1 × 100 = 10%
The population decreased by 10%.
Practice Problem
- If an item's price goes from $75 to $90, what is the percentage increase?
- If a stock value goes from $120 to $108, what is the percentage decrease?
How to Convert Percentages into Decimals?
To convert a percentage to a decimal, divide the percentage by 100. This is equivalent to moving the decimal point two places to the left.
Formula:
Decimal = Percentage / 100
Example: Convert 75% to a decimal.
Solution
75% = 75/100 = 0.75
Example: Convert 20% to a decimal.
20% = 20/100 = 0.20 or simply 0.2.
How to Convert Decimals into Percentages?
To convert a decimal to a percentage, multiply the decimal by 100. This is equivalent to moving the decimal point two places to the right.
Formula:
Percentage = Decimal × 100
Example: Convert 0.5 to a percentage.
Solution: 0.5 × 100 = 50%.
Example: Convert 0.03 to a percentage.
Solution: 0.03 × 100 = 3%
Practice Problems
- Convert 37.5% to a decimal.
- Convert 0.125 to a percentage.
Vikram has a Postgraduate degree in Applied Mathematics, with a keen interest in Data Science and Machine Learning. He has experience of 2+ years in content creation in Mathematics, Statistics, Data Science, and Mac... Read Full Bio
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