correct answer is: c) 7 \large\frac{14}{495}

Explanation

7.0\;\dot2\;\dot8
Here, 7.0\;\dot2\;\dot8 means 7.0282828…

Now, Convert into vulgar fraction, such as 7.0\;\dot2\;\dot8, we can get the answer by adding the non-repeating portion (7.0) with the repeating portion (7.0\;\dot2\;\dot8 ).

We can represent ‘0.0\;\dot2\;\dot8’ as \large\frac{28}{990} because there are two digits repeating, and each digit can range from 0 to 9, making a total of 99 possible combinations. Therefore, 0.028=\large\frac{28}{990}
Now, we add the non-repeating part (7) to the fraction we got from the repeating part:
7+\large\frac{28}{990}
\rightarrow \large\frac{6930+28}{990}
\rightarrow \large\frac{6958}{990}
\rightarrow \large\frac{3479}{495} _[simplify]
\rightarrow 7\large\frac{14}{495}
Ans: 7 \large\frac{14}{495} .

Additional variations of this particular math query are:

1. What is the vulgar fraction form of the decimal 7.028?
2. Find the vulgar fraction equivalent of the decimal 7.028.
3. Convert the decimal 7.028 into a fraction in its simplest form.
4. Convert recurring Decimals 7.028 to fraction.