I have come up with the following method for summing the digits in number. It seems to work for numbers below about 10^23, but doesn't work for higher numbers. Why does it not work for higher numbers?
x=0
for i in range(0, 5000):
x+=((number/10**i)//1)%10
print(x)
Leaving aside that this is a very inefficient way to sum the digits, and assuming you're using Python 3, add a conditional print to the loop:
for i in range(0, 5000):
piece = ((number/10**i)//1)%10
if piece:
print(i, piece)
x+=((number/10**i)//1)%10
Then you'll be able to see where it's going wrong. Starting with number = 10**24, I get output:
0 4.0
1 2.0
24 1.0
7.0
You're not expecting those intermediate results, right? Now you only have to figure out why you're getting them ;-)
The short course is that you're doing floating-point computations when you should be doing integer computations. You get off track immediately (when i is 0):
>>> 10**24/10**0
1e+24
>>> _ // 1
1e+24
>>> _ % 10
4.0
Why is that? Because 10**24 isn't exactly representable as a binary floating-point number:
>>> from decimal import Decimal
>>> Decimal(1e24)
Decimal('999999999999999983222784')
So the exact value of the approximation stored for 1e24 is 999999999999999983222784, and that indeed leaves a remainder of 4 when divided by 10.
To fix this, just stick to integer operations:
number = 10**24
x=0
for i in range(0, 5000):
x += number//10**i % 10
print(x)
That prints 1. Much more efficient is to do, e.g.,
print(sum(int(ch) for ch in str(number)))