Percentages

Percentages are a part of our daily lives, from calculating discounts at the store to determining investment growth. As a mathematical concept, percentages help us quantify a ratio or proportion, expressing it as a fraction of 100. In this article, we will explore various percentage calculation methods and techniques to improve your understanding of this essential mathematical tool.

Fraction To Percent Conversion :

Fractions and percentages are two fundamental ways to represent parts of a whole. In various situations, you might need to convert a fraction to a percentage, such as when comparing data or calculating discounts. In this article, we will provide a step-by-step guide to help you understand the process of converting fractions to percentages with ease.

Basic Percentage Calculation Formula

The most fundamental method of calculating percentages is using the basic percentage formula:

Percentage = (part / total) × 100

Here, the part refers to the value you want to find the percentage of, and the total is the overall value. To find the percentage, divide the part by the total, and then multiply the result by 100.

For example, if you scored 75 out of 100 in a test, your percentage would be:

Percentage = (75 / 100) × 100 = 75%

Finding the Part from a Percentage
If you know the total and the percentage, you can calculate the part. To do this, follow this formula:

Part = (percentage × total) / 100

For example, if you want to find 30% of 150:

Part = (30 × 150) / 100 = 45

Finding the Total from a Percentage
If you have the percentage and the part, you can determine the total by using this formula:

Total = (part × 100) / percentage

For example, if a 45% discount saves you $90, the total original price would be:

Total = (90 × 100) / 45 = $200

Percentage Increase or Decrease
To calculate the percentage increase or decrease between two numbers, use the following formula:

Percentage change = ((new value – old value) / old value) × 100

If the result is positive, it represents an increase, while a negative result indicates a decrease. For example, if your salary increased from $50,000 to $55,000:

Percentage change = ((55,000 – 50,000) / 50,000) × 100 = 10%

Compound Interest Calculations
When dealing with investments, compound interest is an essential concept. The formula for calculating compound interest is:

A = P × (1 + r/n)^(n × t)

Here, A represents the final amount, P is the principal amount, r is the annual interest rate (in decimal form), n is the number of times interest is compounded per year, and t is the time in years. To find the percentage growth, use the percentage increase formula from point 4.

Percentage Error
Percentage error is a way to quantify the difference between an estimated value and the actual value. The formula for percentage error is:

Percentage error = (|estimated value – actual value| / actual value) × 100

For example, if you estimated a project would cost $10,000 but the actual cost was $12,000:

Percentage error = (|$10,000 – $12,000| / $12,000) × 100 = 16.67%

Converting Between Fractions, Decimals, and Percentages
When working with percentages, you may need to convert between fractions, decimals, and percentages. Here are the conversion methods:

To convert a fraction to a percentage, divide the numerator by the denominator and multiply by 100.
To convert a decimal to a percentage, multiply the decimal by 100.
To convert a percentage to a fraction, divide the percentage by 100 and simplify.
To convert a percentage to a decimal, divide the percentage by 100.