stackexchange,
I'm recently trying to get into the p-adic numbers with some materials on the web. I understand the very basics of arithmatics with the p-adic numbers and followed some examples I found as well as calculated some of my own.
So far, however, all the examples I found dealt with primes $p < 11$. I now wonder how to write down p-adic numbers where p is a prime with multiple digits.
For example, given the prime $p = 11$, I can write the number $n = 120$ down as
$n = \sum_{i=0}^{s-1} a_i p^i$
$120 = \cdots + 0*11^2 + 10*11^1 + 10*11^0$
$120 = \cdots 0 10 10$
But if now someone were to only give me the 11-adic number $\cdots 0 10 10$ without any further explanation, how would I know that it is the number 120 and not
$\cdots 0 10 10 = 1*11^3 + 0*11^2 + 1*11^1 + 0*11^0 = 1331 + 0 + 11 + 0 = 1342$ ?
Sadly, all the examples I could find so far in the materials I have use primes $< 10$. Is there a writing convention for this issue in more advanced material on the topic of the p-adic numbers?