To determine the decimal equivalent of [tex]\(\frac{4}{15}\)[/tex], we can convert the fraction into a decimal.
The decimal representation of [tex]\(\frac{4}{15}\)[/tex] is approximately [tex]\(0.26666666666666666\)[/tex], where the 6 repeats indefinitely. This means that after the initial 2, the digit 6 repeats forever. This type of decimal is called a repeating decimal.
Analyzing the given options:
- Option (A) is 0.26. While this number is close to the decimal we need, it is not the same because 6 does not repeat.
- Option (B) is 0.2626. This also starts similarly but then deviates because it does not have the repeating 6 after the 2.
- Option (C) is [tex]\(0.\overline{26}\)[/tex]. This indicates that both the 2 and 6 repeat indefinitely, which is not correct because only the 6 should repeat.
- Option (D) is [tex]\(0.2\overline{6}\)[/tex]. This means that after the initial 2, the 6 repeats indefinitely, which matches exactly with our result of [tex]\(0.26666666666666666\)[/tex].
Hence, the correct answer is:
(D) [tex]\(0.2\overline{6}\)[/tex]
