Suppose I have two real numbers $a$ and $b$ with decimal expansions
$a = \sum_{i=0}^{N_a} a_i 10^i + \sum_{i=1}^\infty a_{-i} 10^{-i}$ and $b = \sum_{i=0}^{N_b} b_i 10^i + \sum_{i=1}^\infty b_{-i} 10^{-i}$ ($a_i, b_i \in \{0,\dots,9\}\; \forall i$).
Is there a general closed formula for the decimal expansions of $a +b$, $a -b$, $a\cdot b$ and $a/b$ (if defined)?