It's important to use parentheses when working with mixed operators because operator precedence can lead to unintended results. In Python, % and // have the same precedence so the expression is evaluated from left to right. Refer to 6.17 in the Python Documentation for more detailed information on language specific precedence.
In your above code, since it's evaluated from left to right, the floor division will always occur before the modulo operation so no ZeroDivsionError can occur. But to answer your question, you can always use a try and catch block to catch the ZeroDivisionError and handle it on your own.
number = int(input())
try:
a = number // 100
b = number // (10 % 10)
c = number % 10
print(a + b + c)
except ZeroDivisionError:
print("Please enter another number that's not a multiple of 10.")
number = int(input())