Lets say I have a $p$-adic number 4|2 (-3, base 5), where 4 is the repeating part, how do I divide this number by, for example, 13 (base 10 so 23 base 5)? Can this be generalized as a formula for any $p$-adic number a|b divided by c, where a is the repeating part, b is the non-repeating part and c is an integer?
I know that the answer of my example, 4|2 (base 5 $p$-adic) divided by 13 (base 10 integer), is the $p$-adic number 1034 without a non_repeating part, but how do I get here?
Any help would be very much appreciated!