To determine the decimal equivalent of the fraction [tex]\(\frac{13}{75}\)[/tex], we need to divide 13 by 75.
Step-by-Step Solution:
1. Calculate [tex]\(\frac{13}{75}\)[/tex]:
[tex]\[
\frac{13}{75} = 0.173333\ldots
\][/tex]
This is a repeating decimal, where the digit 3 continues indefinitely.
2. Now, let's compare this result with the given options to find the correct match:
- (A) [tex]\(0.21\)[/tex]
- This value is 0.21, which is not equivalent to 0.173333...
- (B) [tex]\(0.\overline{21}\)[/tex] (which repeats as 0.212121...)
- This value repeatedly goes 0.21, which is not equivalent to 0.173333...
- (C) [tex]\(0.3\)[/tex]
- This value is 0.3, which is not equivalent to 0.173333...
- (D) [tex]\(0.\overline{3}\)[/tex] (which repeats as 0.33333...)
- This value repeatedly goes 0.33333, which is not equivalent to 0.173333...
- (E) None of the above
- This is the option we consider when none of the other provided options match the result we calculated.
Given our calculation of the division [tex]\(\frac{13}{75} = 0.173333...\)[/tex], it does not match any of the specific values given in options A, B, C, or D. Therefore, the correct choice is:
[tex]\[
\text{(E) None of the above}
\][/tex]
