Let's work through this step by step:
1. We begin with the initial number: [tex]\( 3.64 \)[/tex].
2. Next, we need to add a fraction to this number. The fraction given is [tex]\(\frac{3}{5}\)[/tex].
3. To find the value of the fraction [tex]\(\frac{3}{5}\)[/tex], we perform the division:
[tex]\[
\frac{3}{5} = 0.6
\][/tex]
4. Now, we need to add this fractional value to the initial number:
[tex]\[
3.64 + 0.6
\][/tex]
5. Performing the addition:
[tex]\[
3.64 + 0.6 = 4.24
\][/tex]
Therefore, the result of [tex]\(3.64+\frac{3}{5}\)[/tex] is [tex]\(4.24\)[/tex].