Why 1//0.01 == 99 in Python?

Question

I imagine this is a classic floating point precision question, but I am trying to wrap my head around this result, running 1//0.01 in Python 3.7.5 yields 99.

I imagine it is an expected result, but is there any way to decide when it is safer to use int(1/f) rather than 1//f ?

Answer 1

If this were division with real numbers, 1//0.01 would be exactly 100. Since they are floating-point approximations, though, 0.01 is slightly larger than 1/100, meaning the quotient is slightly smaller than 100. It's this 99.something value that is then floored to 99.

Answer 2

The reasons for this outcome are like you state, and are explained in Is floating point math broken? and many other similar Q&A.

When you know the number of decimals of numerator and denominator, a more reliable way is to multiply those numbers first so they can treated as integers, and then perform integer division on them:

So in your case 1//0.01 should be converted first to 1*100//(0.01*100) which is 100.

In more extreme cases you can still get "unexpected" results. It might be necessary to add a round call to numerator and denominator before performing the integer division:

1 * 100000000000 // round(0.00000000001 * 100000000000) 

But, if this is about working with fixed decimals (money, cents), then consider working with cents as unit, so that all arithmetic can be done as integer arithmetic, and only convert to/from the main monetary unit (dollar) when doing I/O.

Or alternatively, use a library for decimals, like decimal, which:

...provides support for fast correctly-rounded decimal floating point arithmetic.

from decimal import Decimal cent = Decimal(1) / Decimal(100) # Contrary to floating point, this is exactly 0.01 print (Decimal(1) // cent) # 100