What is a Percentage?
A percentage is a way of expressing a number as a fraction of 100. It is denoted using the percent symbol (%). For example, 45% means 45 out of 100, or 45/100.
The Origin of Percentages
The term “percent” comes from the Latin phrase “per centum,” which means “by the hundred.” This reflects the basic idea of percentages as parts out of a hundred, facilitating easier comparison between different values.
Calculating Percentages
Here’s how to calculate a percentage:
- Finding the Percentage of a Number:
To find a percentage of a number, you multiply the number by the percentage (converted to a decimal).
Formula: Percentage of a number=(Percentage×Total number)/100
Example: Find 20% of 50.
====>> 20% of 50=(20×50)/100=10
- Finding What Percentage One Number is of Another:
To determine what percentage one number is of another, divide the first number by the second number and multiply by 100.
Formula: Percentage=(WholePart)×100
Example: What percentage is 15 of 60?
====>> 60/15×100=25%
- Percentage Increase and Decrease:
- Percentage Increase: The amount by which a number increases, expressed as a percentage of the original number.
Formula: Percentage Increase={(New Value−Original Value)/Original Value}×100
- Percentage Increase: The amount by which a number increases, expressed as a percentage of the original number.
If a price rises from $50 to $60, the increase is:
====>> {(60-50)/50} x 100 = 20%
- Percentage Decrease: The amount by which a number decreases, represented as a percentage of the original number.
Formula: Percentage Decrease={(Original Value−New Value)/Original Value}×100
If a price drops from $80 to $60, the decrease is:
====>> {(80-60)/80}x100 = 25%
Applications of Percentages
Percentages are used in various fields, including:
- Finance: Interest rates, discounts, and markups are commonly expressed in percentages.
- Statistics: Percentages help in reporting data and trends, such as population growth or survey results.
- Everyday Life: Percentages are frequently encountered in promotions, tax calculations, and tips in restaurants.
Key Points to Remember
- A percentage is always based on a total of 100.
- To convert a percentage to a decimal, divide by 100.
- Be cautious with operations involving percentages, particularly when dealing with multiple percentage changes in succession, as they can compound in complex ways.
Practical Example
Scenario: If you have a salary of $50,000 and expect a 10% raise, you can find the new salary as follows:
- Calculate the raise:
Raise=10% of 50000=(10/100)×50000=5000
- Add it to the original salary:
New Salary=50000+5000=55000
Conclusion
Percentages are a fundamental concept in mathematics that allow us to express ratios and comparisons effectively. Understanding how to calculate and apply percentages is essential for everyday activities, from managing finances to interpreting statistical data.