Answer
$$\dfrac{4}{9}$$
Work Step by Step
We have: $0.4444......=0.4+0.04+....=\Sigma_{n=1}^{\infty} 0.4 (0.1)^{n-1}$
This shows a geometric series with common ratio $r=0.1$ and with initial term $a=0.4$. We see that $|r| \lt 1$, so the series converges.
Therefore, the sum is: $$0.4444=\dfrac{a}{1-r}\\=\dfrac{0.4}{1-0.1}\\=\dfrac{4}{9}$$
