To solve the fraction [tex]\(\frac{2}{3}\)[/tex], we'll find its decimal representation.
Step-by-Step Solution:
1. Understand the Fraction: [tex]\(\frac{2}{3}\)[/tex] represents dividing the numerator, which is 2, by the denominator, which is 3.
2. Perform Division: To convert this fraction to a decimal, divide 2 by 3 using long division or a calculator.
3. Result: The result of dividing 2 by 3 gives us a repeating decimal. Specifically,
[tex]\[
\frac{2}{3} \approx 0.6666666666666666
\][/tex]
where the digit 6 repeats indefinitely.
Therefore, the decimal representation of the fraction [tex]\(\frac{2}{3}\)[/tex] is approximately [tex]\(0.6666666666666666\)[/tex]. This can also be expressed as [tex]\(0.\overline{6}\)[/tex], indicating that the digit 6 repeats infinitely.
