17 over 20 as a percentage is 85%.
Understanding how to convert fractions to percentages is a fundamental mathematical skill that allows for clear comparison and representation of values.
What is a Percentage?
A percentage is a way of expressing a number as a fraction of 100. The word "percentage" comes from "per cent," which literally means "per hundred." It's denoted by the percent sign (%). For instance, 25% means 25 out of 100, or 25/100, which simplifies to 1/4. Percentages are widely used to describe proportions, ratios, and changes in a standardized format.
How to Convert a Fraction to a Percentage
Converting a fraction to a percentage involves a simple two-step process:
- Convert the fraction to a decimal: Divide the numerator (the top number) by the denominator (the bottom number).
- Convert the decimal to a percentage: Multiply the resulting decimal by 100.
This method allows any fraction to be expressed as a value out of 100, making it easier to understand its proportion relative to a whole. For more detailed insights into converting fractions to percentages, you can refer to educational resources like Khan Academy's guide on fractions to percents.
Step-by-Step Conversion of 17/20
Let's apply these steps to convert 17 over 20 into a percentage:
-
Divide the numerator by the denominator:
- Numerator = 17
- Denominator = 20
- 17 ÷ 20 = 0.85
-
Multiply the decimal by 100:
- 0.85 × 100 = 85
Therefore, 17 over 20 as a percentage is 85%.
Practical Applications of Percentage Conversion
Converting fractions to percentages is not just a mathematical exercise; it has numerous real-world applications that help in understanding data and making informed decisions.
- Academic Grades: If you score 17 correct answers out of a possible 20 questions on a test, your grade is 85%. This allows for easy comparison with other test scores or grading scales.
- Discounts and Sales: A store offering "17 out of 20" off the original price means you are getting an 85% discount, which is a significant saving.
- Financial Reporting: Understanding percentages is crucial for interpreting financial statements, such as growth rates, interest rates, and profit margins. For instance, a return of 17 dollars for every 20 dollars invested represents an 85% return on investment.
- Survey Results: If 17 out of 20 people prefer a certain product, it's often reported as 85% of respondents.
Common Fraction-to-Percentage Conversions
Here are a few common examples to illustrate the concept:
| Fraction | Decimal Conversion | Percentage |
|---|---|---|
| 1/2 | 0.50 | 50% |
| 3/4 | 0.75 | 75% |
| 4/5 | 0.80 | 80% |
| 1/10 | 0.10 | 10% |
