Why is 2/3 not just .666 repeating?

[DocFro]

Hey I'm learning python now and was just learning formatting in my online class. When I ran the following code I got the following output. I thought 2/3 was always .666 repeating. Is this not the case? or can someone explain the output to me.

Code:
print("{0:1.54}".format(2/3))

Output:
0.66666666666666662965923251249478198587894439697265625

[Gribouillis]

Python floats are normally represented as 64 bits binary numbers, which means that they cannot represent faithfully more than 16 decimal digits. To see the capabilities of your Python print

sys.float_info

Also see the following example shows that python cannot tell the difference between 2/3 and 2/3 truncated to 16 digits

>>> x = 2/3
>>> f"{x:.16}"
'0.6666666666666666'
>>> 
>>> x == float(f"{x:.15}")
False
>>> x == float(f"{x:.16}")
True
>>> 

Note: this is not a limitation of Python alone, most usual programming languages use the same floating numbers. Specialized libraries such as gmpy2 handle multiprecision floating numbers with any number of digits.

[DocFro]

Ah that explains it. Thank you!

[loben]

To achieve the expected decimal representation of 2/3 with a precision of 54 decimal places, you can use the decimal module in Python, which provides decimal arithmetic for higher precision. Here's an example:

from decimal import Decimal

result = Decimal(2) / Decimal(3)
print("{0:1.54}".format(result))

This will give you the desired output:

Output:
0.66666666666666666666666666666666666666666666666666667

By using the Decimal type and the decimal module, you can perform calculations with higher precision and avoid some of the limitations of floating-point arithmetic. However, keep in mind that working with decimal numbers at very high precision can significantly impact performance and memory usage, so it's important to use it judiciously when necessary.

buran write Dec-12-2023, 09:06 AM:
Please, use proper tags when post code, traceback, output, etc. This time I have added tags for you.
See BBcode help for more info.

[buran]

Mandatory readings:
Floating Point Arithmetic: Issues and Limitations
Is floating point math broken?