11/20 as a decimal is 0.55.
Converting a fraction to a decimal is a fundamental skill in mathematics that allows for easier comparison and calculation. A fraction represents a part of a whole, and its decimal equivalent expresses that same value in a base-10 system.
Understanding Fraction-to-Decimal Conversion
To convert any common fraction like 11/20 into its decimal form, you can use one of two primary methods: division or finding an equivalent fraction with a power of 10 in the denominator. Both methods will yield the same result.
Method 1: Division
The most straightforward way to convert a fraction to a decimal is to divide the numerator by the denominator.
For the fraction 11/20:
| Step | Operation | Result | Explanation |
|---|---|---|---|
| 1 | Divide 11 by 20 | 0 with a remainder of 11 | 20 does not go into 11, so write 0 and a decimal point. |
| 2 | Add a zero to 11 (making it 110) and continue dividing. | 0.5 with a remainder of 10 | 20 goes into 110 five times (20 × 5 = 100). |
| 3 | Add another zero to 10 (making it 100) and continue dividing. | 0.55 with a remainder of 0 | 20 goes into 100 five times (20 × 5 = 100). |
Therefore, 11 ÷ 20 = 0.55.
Method 2: Equivalent Fractions
This method involves converting the fraction into an equivalent fraction where the denominator is a power of 10 (such as 10, 100, 1000, etc.). Once the denominator is a power of 10, the numerator directly gives the decimal value.
For 11/20:
- Identify a multiplier: Determine what number you can multiply the denominator (20) by to get 10, 100, or 1000. In this case, multiplying 20 by 5 will give 100.
- Multiply both numerator and denominator: To keep the fraction equivalent, you must multiply both the numerator and the denominator by the same number (5).
$$ \frac{11}{20} \times \frac{5}{5} = \frac{11 \times 5}{20 \times 5} = \frac{55}{100} $$ - Convert to decimal: The fraction 55/100 means "fifty-five hundredths," which is written as 0.55 in decimal form. The number of zeros in the denominator (100 has two zeros) corresponds to the number of decimal places.
Practical Applications and Examples
Converting fractions to decimals is useful in many real-world scenarios, such as:
- Financial calculations: Understanding interest rates, discounts, or shares.
- Measurement: Converting recipes (e.g., 3/4 cup vs. 0.75 cups), or interpreting engineering specifications.
- Data analysis: Expressing proportions or probabilities in a standardized format.
Here are a few more examples of fraction-to-decimal conversions:
- 1/2 as a decimal:
- 1 ÷ 2 = 0.5
- (1/2) × (5/5) = 5/10 = 0.5
- 3/4 as a decimal:
- 3 ÷ 4 = 0.75
- (3/4) × (25/25) = 75/100 = 0.75
- 1/8 as a decimal:
- 1 ÷ 8 = 0.125
- (1/8) × (125/125) = 125/1000 = 0.125
For further reading on converting fractions to decimals, you can explore resources like Khan Academy.
