Answer :
To find the percentage that is equivalent to [tex]\(\frac{2}{3}\)[/tex], we can follow these steps:
1. Convert the fraction to a decimal:
Divide the numerator (2) by the denominator (3):
[tex]\[
\frac{2}{3} = 0.66666666\ldots
\][/tex]
This is a repeating decimal.
2. Convert the decimal to a percentage:
To convert a decimal to a percentage, multiply it by 100:
[tex]\[
0.66666666\ldots \times 100 = 66.666666\ldots\%
\][/tex]
3. Express the repeating decimal as a fraction:
The decimal 0.666666\ldots is equivalent to [tex]\(66 \frac{2}{3}\%\)[/tex] because the repeating decimal 0.666... is equivalent to the fraction [tex]\(\frac{2}{3}\)[/tex].
So, the percentage 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]
1. Convert the fraction to a decimal:
Divide the numerator (2) by the denominator (3):
[tex]\[
\frac{2}{3} = 0.66666666\ldots
\][/tex]
This is a repeating decimal.
2. Convert the decimal to a percentage:
To convert a decimal to a percentage, multiply it by 100:
[tex]\[
0.66666666\ldots \times 100 = 66.666666\ldots\%
\][/tex]
3. Express the repeating decimal as a fraction:
The decimal 0.666666\ldots is equivalent to [tex]\(66 \frac{2}{3}\%\)[/tex] because the repeating decimal 0.666... is equivalent to the fraction [tex]\(\frac{2}{3}\)[/tex].
So, the percentage 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]
