How many zeros does it take?

Question

Print(10 < 10.1) outputs True, of course, but print(10 < 10.000000000000000000000000001) outputs False

Why can I see when numbers are unequal but the computer can't?

I wrote this little code to pin down the number of zeros required to produce False, but it times out, and I'm not sure if the problem is my code or the platform. Thoughts welcome!!

def num_of_zeros(n):
i = 0
a = float("10." + "0" * i + str(n))
while (10 < a):
i += 1
print(i)

num_of_zeros(1)

Answer 1

here it is in the code playground. it runs fine, no timeouts

https://code.sololearn.com/c68AXldXdmGM/?ref=app

Answer 2

@Kyle
Thanks - now I've got it. I should have put a = float("10." + "0" * i + str(n)) inside the loop. I revised the code (and gave you a credit).

https://code.sololearn.com/c6hPk05yqx9X/#py

Answer 3

@Kyle I'm not sure that's correct. The function prints i, not a. To test your theory, I shortened the number of loop cycles (because it times out on the code playground) by using
while (10 < a and i < 2):
instead of
while (10 < a):
and got the output 2

Answer 4

Happy to help David.. Keep up the good work!

Answer 5

David.. Your code output is
10.1
10.1
10.1
10.1
etc

The reason being you change I, but you don't change a.. Perhaps this will help.

def num_of_zeros(n):
i = 0
a = float("10." + "0" * i + str(n))
while (10 < a):
a = float("10." + "0" * i + str(n))
print(a)
i += 1
print(i)

num_of_zeros(1)

Answer 6

correct. but a is your number 10.0 + number of zeros. you print i after it's done to show how many runs it does. I print a inside your loop just to show the progress. my output is

10.1
10.01
10.001
etc.

And when it is done running, it has your I listed as 16..

The only difference between my code and yours is that mine adds a 0 each time it runs where as yours runs indefinitely at 10.1