A fifth of 100 is 20, and when expressed as a percentage, this is 20%.
Understanding a Fifth of 100
To determine "a fifth of 100," we perform a simple calculation involving fractions or division. This means taking one part out of five equal parts of the number 100.
- Fraction Calculation:
$$ \frac{1}{5} \times 100 = \frac{100}{5} = 20 $$
Therefore, a fifth of 100 is 20.
Expressing the Result as a Percentage
The term "percentage" literally translates to "per hundred" or "out of one hundred." It's a way to express a part of a whole as a fraction of 100.
Since we found that a fifth of 100 is 20, and the question asks for this value "in percentage" (implying its proportion relative to the original 100), the conversion is straightforward:
- Direct Conversion: If a specific value is 20 out of a total of 100, it inherently represents 20% of that total.
- Formulaic Percentage Conversion: To convert any part of a total into a percentage, you can use the formula:
$$ \text{Percentage} = \left( \frac{\text{Part}}{\text{Total}} \right) \times 100\% $$
In this scenario, the "Part" is 20 (which is a fifth of 100) and the "Total" we are comparing it to is 100.
$$ \text{Percentage} = \left( \frac{20}{100} \right) \times 100\% = 0.20 \times 100\% = 20\% $$
It's a fundamental concept in mathematics that one-fifth (1/5) is equivalent to 20%. This direct conversion is widely used and demonstrates the clear relationship between common fractions and their percentage counterparts. For instance, if you divide any whole into 5 equal sections, each section will constitute 20% of the entire whole.
Step-by-Step Calculation
Here’s a clear breakdown of the steps involved:
- Identify the Fraction: The phrase "a fifth" indicates the fraction ( \frac{1}{5} ).
- Calculate the Value: Multiply this fraction by the given number (100): ( \frac{1}{5} \times 100 = 20 ).
- Convert to Percentage: Since percentages are expressed "out of 100," a value of 20 out of 100 directly translates to 20%.
Summary Table
| Step | Calculation | Result |
|---|---|---|
| 1. Find a fifth of 100 | ( \frac{1}{5} \times 100 ) | 20 |
| 2. Express as Percentage | ( \frac{20}{100} \times 100\% ) | 20% |
Practical Applications of Percentages
Proficiency in calculating fractions and converting them into percentages is a vital skill applicable in numerous real-world scenarios:
- Retail Discounts: Quickly determine savings when a store offers a 20% discount on an item.
- Financial Literacy: Understand interest rates on loans, investment returns, or changes in stock prices.
- Data Interpretation: Analyze statistical data, such as market share, survey results, or population demographics, often presented in percentages.
- Culinary Adjustments: Scale recipes by a certain percentage when you need to make more or less than the original yield.
- Academic Performance: Calculate test scores or grade percentages to understand your academic standing.
To further enhance your understanding of how to convert fractions to percentages and grasp other fundamental percentage concepts, exploring comprehensive educational resources can be very beneficial.
