Answer
$$\dfrac{44663}{99000}$$
Work Step by Step
We have: $0.451141414......=0.451+0.00014+......=0.451+\Sigma_{n=1}^{\infty} 0.00014 (0.01)^{n-1}$
This shows a geometric series with common ratio $r=0.01$ and with initial term $a=0.00014$. We see that $|r| \lt 1$, so the series converges.
Therefore, the sum is: $$5.373737=0.451+\dfrac{a}{1-r}\\=0.451+\dfrac{0.00014}{1-0.01}\\=\dfrac{44663}{99}$$
