Converting 20 percent involves transforming it from its percentage form into both a fraction and a decimal. Specifically, 20% can be converted to the simplified fraction 1/5 or the decimal 0.2.
Understanding Percentages
A percentage represents a part per hundred. The term "percent" literally means "per one hundred." Therefore, any percentage can be initially written as a fraction with a denominator of 100.
Converting 20 Percent to a Fraction
To convert a percentage to a fraction, you simply place the percentage value over 100. Once it's in fraction form, you can then simplify it to its lowest terms.
- Step 1: Write as a fraction over 100.
- 20% = 20/100
- Step 2: Simplify the fraction.
- Divide both the numerator and the denominator by their greatest common divisor. In this case, both 20 and 100 are divisible by 10:
- 20 ÷ 10 = 2
- 100 ÷ 10 = 10
- This gives us 2/10
- Further simplify by dividing both by 2:
- 2 ÷ 2 = 1
- 10 ÷ 2 = 5
- This results in the simplified fraction 1/5
- Divide both the numerator and the denominator by their greatest common divisor. In this case, both 20 and 100 are divisible by 10:
Fraction Conversion Summary
| Percentage | Fraction over 100 | Simplified Fraction |
|---|---|---|
| 20% | 20/100 | 1/5 |
Converting 20 Percent to a Decimal
There are two primary ways to convert a percentage to a decimal: by dividing by 100 or by converting its fractional form.
- Method 1: Divide by 100.
- Since a percentage is "per one hundred," dividing the percentage value by 100 directly yields its decimal equivalent.
- 20 ÷ 100 = 0.2
- Method 2: Convert from the simplified fraction.
- Once you have the simplified fraction (1/5), you can perform the division of the numerator by the denominator.
- 1 ÷ 5 = 0.2
Decimal Conversion Summary
| Percentage | Division by 100 | From Simplified Fraction | Decimal Equivalent |
|---|---|---|---|
| 20% | 20 ÷ 100 | 1 ÷ 5 | 0.2 |
Practical Applications of Percentages
Understanding how to convert percentages is fundamental in many real-world scenarios:
- Financial Calculations: Calculating discounts (e.g., a 20% off sale), interest rates, or tips.
- Example: A \$50 item with a 20% discount means you save \$50 * 0.2 = \$10.
- Statistics and Data Analysis: Expressing proportions or changes in data.
- Academic Grades: Often represented as percentages.
- Recipes: Adjusting ingredient quantities based on percentages.
By mastering these simple conversions, you can easily interpret and apply percentage information in various contexts.
