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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]68 \frac{7}{10} \%[/tex]

Answer :

To find 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 it step-by-step:

1. Understand the Relationship:
- A percentage is essentially a fraction out of 100. So, to express [tex]\(\frac{2}{3}\)[/tex] as a percent, we need to find an equivalent fraction with a denominator of 100.

2. Convert the Fraction to a Percentage:
- Multiply the fraction [tex]\(\frac{2}{3}\)[/tex] by 100, because a percentage is a way to express a number as a part of 100.

[tex]\[
\frac{2}{3} \times 100 = \frac{200}{3}
\][/tex]

3. Perform the Division:
- Divide 200 by 3 to get the decimal form:

[tex]\[
200 \div 3 = 66.6666\ldots
\][/tex]

This result repeats with the digit 6.

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

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

Therefore, the correct answer is:

[tex]\[ 66 \frac{2}{3} \% \][/tex]

This matches the option: [tex]\(66 \frac{2}{3} \%\)[/tex].

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