True of False

Question

Why is this False:
a = 3**45 == int(float(3**45))
print(a)

When this is True:
a = 3**3 == int(float(3**3))
print(a)

I don't understand this logic.

Answer 1

It is linked to something called limited floating point accuracy or precision:
https://en.m.wikipedia.org/wiki/Floating-point_arithmetic#Accuracy_problems

Basically, floats in their decimal state have to be represented by binary system (deep, deep down in the "computer core" :)

This causes problems for all numbers which cannot be precisely represented using powers of 2 - so basically most real numbers.

float(3) is represented by a number closest to its representation (it might be something like 3.000000000000000004) which for "small" computations makes no difference, but for large operations likes exponentiation, the inaccuracy might result in a bit different, unexpectedly different, number.

Please note that for numbers which are exactly the power of 2, this does not happen.

4.0**100 == 4**100

Answer 2

Try printing this
print(int(float(3**34)))
print(3**34)

Answer 3

It only started changing at 3**34.

Higher level (or lower level) SoloLearners who always gets this question right in the challenge section, come and explain it o!!!

Answer 4

Abhay I still do not understand.

Have you tried this:
print(int(float(3**33)))
print(3**33)

Does it mean for larger exponentials, it changes or something?