Select the decimal that is equivalent to [tex]\frac{13}{75}[/tex].

Choose 1 answer:

A. 0.21
B. [tex]0 . \overline{21}[/tex]
C. 0.3
D. [tex]0 . \overline{3}[/tex]
E. None of the above



Answer :

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]