Consider $\frac1{101}=0.00990099\dots$ and $\frac1{143}=0.00699300699300\dots$ and $\frac1{101\times 143}=0.0000692376930000692376930000\dots$.
Now $990\times69930=69230700$ which is almost $69237693$.
Is it possible to get exact equality? If so when should I truncate the fractions before multiplying?
No. You ask whether it is possible to have $$\frac a{10^n-1}\cdot\frac b{10^m-1}=\frac{ab}{10^k-1}. $$ Except for the trivial cases $a=0$ or $b=0$, this would require $$ 10^k-1=(10^n-1)(10^m-1)=10^{n+m}-10^n-10^m+1.$$ As the left is $\equiv-1\pmod {10}$ and the right $\equiv +1\pmod{10}$, this cannot happen.