Mod- unexpected result

[bryann]

I am getting an unexpected result when using mod '%' in Python.
When I type

print(356%3.56)

I would expect the result to be 0 as 3.56 goes in to 356 exactly 100 times. However when I run the code it returns 3.5599999999999947.
What is the reason for returning this number and not 0?

Thanks in advance

[cereal]

Hi,

It happens because of rounding errors, for more information see:

• http://floating-point-gui.de/
• http://docs.oracle.com/cd/E19957-01/806-3568/ncg_goldberg.html

You could try with Decimal():

from decimal import Decimal

# with binary floating points
print(divmod(356, 3.56))
(99.0, 3.5599999999999947)

# with arbitrary roundings
print(Decimal('356') % Decimal('3.56'))
0.0

Example: http://ideone.com/a6UDRi

[bryann]

Great! thanks for your help

[Gribouillis]

On my computer, when I write

f = 3.56

in a python program, the following bits are stored in memory

0 10000000000 1100011110101110000101000111101011100001010001111011

This is the IEEE 754 representation of the floating point number 3.56 according to my machine's precision. The corresponding real value is not exactly 3.56, it is

Fraction(8016407336719483, 2251799813685248)

This is equal to

Fraction(356, 100) + Fraction(3, 56294995342131200)

The error is approximately 5.3290705182e-17

Also have a look at https://docs.python.org/3/tutorial/floatingpoint.html