Change the following mixed number to a percent. Write your answer in percent form. Round your answer to the nearest tenth of a percent, if necessary.
$2 \frac{3}{50}$
Answer (1)
Convert the mixed number to an improper fraction: 2 50 3 = 50 103 .
Convert the improper fraction to a decimal: 50 103 = 2.06 .
Convert the decimal to a percentage: 2.06 × 100 = 206% .
The final answer is 206.0% .
Explanation
Understanding the Problem We are asked to convert the mixed number 2 50 3 to a percent. To do this, we first convert the mixed number to a decimal, and then multiply by 100 to express it as a percentage.
Converting to an Improper Fraction First, convert the mixed number 2 50 3 to an improper fraction. We have: 2 50 3 = 50 2 × 50 + 3 = 50 100 + 3 = 50 103
Converting to a Decimal Next, convert the improper fraction 50 103 to a decimal. We can do this by dividing 103 by 50: 50 103 = 2.06
Converting to a Percentage Now, convert the decimal 2.06 to a percentage by multiplying by 100: 2.06 × 100 = 206 So, 2.06 = 206% .
Final Answer The percentage is already to the nearest tenth of a percent, since it is a whole number. Therefore, the final answer is 206.0% .
Examples
In everyday life, converting mixed numbers to percentages is useful in various scenarios, such as calculating discounts or understanding proportions. For example, if a store offers a discount of 2 50 3 off the original price, converting this to a percentage helps you quickly understand the discount amount. In this case, 2 50 3 is equal to 206%, which means you'd be paying 206% of the original price (not a typical discount scenario, but mathematically valid!). Understanding these conversions helps in making informed decisions in shopping, finance, and other areas.
