Definition
Percent and Percentage are statistical terms used to express a ratio or fraction where the whole is represented by the number 100. A percent (%) indicates a part out of 100 and is commonly used in various fields such as finance, economics, statistics, and general arithmetic to compare and report changes, distributions, and proportions.
Key Points:
- Percent (%): Symbolic representation of a fraction of 100.
- Percentage: Refers to the result obtained when multiplying a number by a percent.
Examples
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Interest Rates:
- If a bank offers 5% interest on savings annually, for every $100 deposited, $5 will be earned in interest after one year.
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Price Changes:
- A product originally costing $50 is now on sale for 20% less. The discount amount is \( 50 * 0.20 = $10 \), so the sale price is \( $50 - $10 = $40 \).
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Income Allocation:
- If a person allocates 30% of their monthly income to housing costs, and their monthly income is $3000, they will spend \( 3000 * 0.30 = $900 \) on housing.
Frequently Asked Questions (FAQs)
What is the difference between percent and percentage?
Percent is used to denote a value out of 100 and is often followed by a specific number (e.g., 50%). Percentage refers to a rate, number, or amount in each hundred, and is a more general term often used without a specific numeric value directly attached.
How do you calculate a percentage?
To calculate a percentage, divide the part by the whole and then multiply by 100: \[ \text{Percentage} = \left( \frac{\text{Part}}{\text{Whole}} \right) * 100 \]
Why is the percent sign (%) used?
The percent sign (%) is used for convenience to represent a ratio as part of 100 directly. For instance, 25% is easier to recognize and understand than writing 25 out of 100 or 0.25.
What is the difference between percentage increase and percentage decrease?
A percentage increase shows how much a value has risen in terms; a percentage decrease shows how much a value has dropped. The formulas are: \[ \text{Percentage Increase} = \left( \frac{\text{New Value} - \text{Original Value}}{\text{Original Value}} \right) * 100 \] \[ \text{Percentage Decrease} = \left( \frac{\text{Original Value} - \text{New Value}}{\text{Original Value}} \right) * 100 \]
How are percentages used in financial markets?
Percentages are crucial in financial markets for expressing interest rates, profit margins, growth rates, and price fluctuations. They enable standardization and easier comparison across different scales and periods.
How do you express a number as a percentage of another number?
To express a number as a percentage of another number, divide the first number by the second number, then multiply by 100: \[ \text{Percentage of A out of B} = \left( \frac{A}{B} \right) * 100 \]
Related Terms
- Ratio: A representation of the relative size of two quantities, expressed as the quotient of one divided by the other.
- Fraction: A numerical quantity that is not a whole number, representing a part of a whole.
- Decimal: A number expressed using a system of numeric notation based on the powers of ten.
- Proportion: A part, share, or number considered in comparative relation to a whole.
Online Resources
Suggested Books for Further Studies
- “Mathematics for Business and Social Sciences” by Raymond A. Barnett
- “Practical Business Math Procedures” by Jeffrey Slater
- “Statistics for Business and Economics” by Paul Newbold, William L. Carlson, Betty Thorne
Fundamentals of Percent and Percentage: Statistics Basics Quiz
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