Be careful about the notation for modular arithmetic. Usually, people write a ≡ b mod n, or [a] = [b], where it is understood that [a] is the congruence class of a modulo n (i.e. the equivalence class of a w.r.t the relation bRc iff b ≡ c mod n).

When you write the decimal expansion of a number, say it with a sentence in plain English, e.g: " Let c_{0}10^{0} + c_{1}10^{1} + ... + c_{k} 10^{k} be the decimal expansion of n " is better than
" n = c_{0}10^{0} + c_{1}10^{1} + ... + c_{k} 10^{k} " (for all I know, in the second case, the c_{i} could be arbitrary real numbers.
This also makes it implicitly clear that you are using existence and uniqueness of the decimal expansion).