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\( 8.5 \% \) is equivalent to what fraction in reduced terms?

Ask by Brewer Todd. in the United States
Feb 03,2025

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\( 8.5\% \) is equal to \( \frac{17}{200} \).

Solución

To convert \( 8.5\% \) to a fraction in its simplest form, follow these steps: 1. **Understand the Percentage:** \[ 8.5\% = \frac{8.5}{100} \] 2. **Eliminate the Decimal:** Multiply both the numerator and denominator by 10 to remove the decimal: \[ \frac{8.5 \times 10}{100 \times 10} = \frac{85}{1000} \] 3. **Simplify the Fraction:** Find the greatest common divisor (GCD) of 85 and 1000, which is 5. \[ \frac{85 \div 5}{1000 \div 5} = \frac{17}{200} \] So, \( 8.5\% \) as a reduced fraction is: \[ \frac{17}{200} \]

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Bonus Knowledge

To convert \( 8.5\% \) into a fraction, start by writing it as \( \frac{8.5}{100} \). To eliminate the decimal, multiply the numerator and denominator by \( 10 \), resulting in \( \frac{85}{1000} \). Now, you can simplify this fraction. Both \( 85 \) and \( 1000 \) are divisible by \( 5 \), yielding \( \frac{17}{200} \). So, in reduced terms, \( 8.5\% \) is equivalent to \( \frac{17}{200} \). Fun fact: percentages are really just fractions with a denominator of \( 100 \)! The term "percent" literally means "per hundred" in Latin, showing just how interconnected numbers can be. It’s like speaking math with flair! Additionally, checking your work is key! It’s a common pitfall to overlook simplifying fractions correctly. Always ensure that you’ve divided by the greatest common divisor—this is like giving your fraction a fresh outfit so it looks its best!

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