Answer :

Let's solve the problem step-by-step to find the decimal equivalent of the fraction \(\frac{13}{20}\).

1. Understand the fraction: We need to convert the fraction \(\frac{13}{20}\) into a decimal format.

2. Division of the numerator by the denominator: To convert a fraction to a decimal, you divide the numerator (the top number) by the denominator (the bottom number).
[tex]\[ \frac{13}{20} \][/tex]

3. Perform the division: When you divide 13 by 20, you get the following:
[tex]\[ 13 \div 20 = 0.65 \][/tex]

4. Verify the result with the provided choices:
- Option A is 0.065
- Option B is 0.65
- Option C is 0.15
- Option D is 0.015

5. Match the division result to the options: The calculated decimal result is 0.65, which matches option B.

So, the best answer to the question is:
[tex]\[ \boxed{0.65} \][/tex]

Hence, the correct choice is:
[tex]\[ \boxed{B} \][/tex]