Percentage Calculator

What is a Percentage?

A percentage is a way to express numbers as a fraction of 100. The word comes from the Latin "per centum", meaning "by the hundred". Percentages are ubiquitous in our daily lives - from shopping discounts and tax calculations to statistics and financial reports.

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Basic Concept

One percentage point (1%) represents one-hundredth of a whole. It can be written as:

1. 1% = 1/100 = 0.01

For example, if 25% of students in a class are left-handed, it means that 25 out of every 100 students are left-handed, or one-quarter of the total.

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Percentage Formulas

There are three basic percentage calculations:

1. Finding what percentage X is of Y: (X ÷ Y) × 100 = percentage
2. Finding what is X% of Y: Y × (X ÷ 100) = result
3. Finding X is what percent of what number: X ÷ (percentage ÷ 100) = result

Practical Applications of Percentages

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Shopping and Discounts

When you see an item priced at $50 with a 30% discount, you can calculate the savings as $50 × 0.3 = $15, making the final price $35.

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Financial Calculations

Percentages are crucial for understanding interest rates, taxes, and investment returns. For example, if your investment grew by 8% last year, a $1,000 investment would have increased by $80.

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Academic Scoring

Exam results are typically expressed as percentages to standardize evaluation across assessments with different total points.

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Health and Nutrition

Nutritional information on food packaging uses percentages to show how much of your daily recommended intake of various nutrients is contained in one serving.

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Statistics and Data Analysis

Surveys and research studies often present findings in percentages to make data more comparable and easier to understand.

Tips for Working with Percentages

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Quick Mental Math

1. To find 10% of a number, simply move the decimal point one place to the left.
2. For 5%, take half of 10%.
3. For 1%, divide 10% by 10.
4. For 25%, take a quarter of the number or divide by 4.
5. For 50%, divide by 2.
6. For other percentages, break them down into combinations of these easier values.

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Understanding Percentage Change

When something increases from 100 to 150, that's a 50% increase. But when it decreases from 150 back to 100, that's only a 33.33% decrease. This asymmetry can sometimes be confusing but is important to understand in financial contexts.

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