College

What percent is equivalent to [tex]\frac{2}{3}[/tex]?

A. [tex]66 \frac{1}{3} \%[/tex]
B. [tex]66 \frac{3}{5} \%[/tex]
C. [tex]66 \frac{2}{3} \%[/tex]
D. [tex]66 \frac{7}{203} \%[/tex]

Answer :

To determine what percent is equivalent to the fraction [tex]\(\frac{2}{3}\)[/tex], we need to convert the fraction into a percentage. Here’s how you can do that step-by-step:

1. Understand the Relationship Between Fractions and Percentages:
- A percentage is a fraction out of 100. So, to convert a fraction to a percentage, you can multiply by 100.

2. Convert the Fraction to a Percentage:
- Take the fraction [tex]\(\frac{2}{3}\)[/tex] and multiply it by 100 to find its percentage equivalent:
[tex]\[
\frac{2}{3} \times 100 = \frac{200}{3} = 66.6666\ldots
\][/tex]
- This result is a repeating decimal, specifically [tex]\(66.6666\ldots\)[/tex].

3. Express the Result as a Mixed Number:
- The repeating decimal [tex]\(66.6666\ldots\)[/tex] can be expressed as the mixed number [tex]\(66 \frac{2}{3}\%\)[/tex].

4. Identify the Correct Answer:
- From the given options, the one that matches is [tex]\(66 \frac{2}{3}\%\)[/tex].

Thus, the percent equivalent to [tex]\(\frac{2}{3}\)[/tex] is [tex]\(66 \frac{2}{3}\%\)[/tex].