CODEWITHSUNDEEP
pythonfloating-pointint
Kirty Bhushan
Kirty Bhushan

Reputation: 147

Why does print int (100*(11.20 - 11)) prints 19 instead of 20 in python?

I have just started python tutorials. Why does 

print  int (100*(11.20 - 11))

print 19 instead of 20 in python ?? There is some sort of rounding off done by integer but i am unable to catch that. Help is appreciated.

Upvotes: 2

Views: 213

Answers (4)

Tom
Tom

Reputation: 22841

In Python int() truncates toward 0 for reasons Guido explains here. This means negative numbers will actually see the opposite effect (related SO question & answer).

Upvotes: 1

Pascal Cuoq
Pascal Cuoq

Reputation: 80325

This happens because 11.20 is not exactly 1120/100 but slightly less than that. So 11.20 - 11 ends up slightly less than 20/100 (*). Multiplied by 100, 11.20 - 11 produces a floating-point number slightly below 20, and since int(...) truncates (rounds towards zero), the result is 19.

For efficiency reasons, floating-point numbers are represented as fractions with a power of two as the denominator. So 1/2, 1/4, 1/16, … can be represented exactly as floating-point numbers, but 1/5 cannot (there is no power of two that can be used as the denominator to represent 1/5 exactly).

(*) This floating-point subtraction happens to be exact, so that the absolute error of the result compared to 20/100 is exactly the same as the absolute error of 11.20 compared to 1120/100. Note that the relative error is magnified, because the same absolute error is applied to a much smaller value. The subtraction of values that are already inexact and are close is called “catastrophic cancellation”, and the subtraction in your Python line is one such catastrophic cancellation.

Upvotes: 7

njzk2
njzk2

Reputation: 39406

As said, it is a rounding issue with floating points precision. You can see that using :

print '%.20f' % (100*(11.20 - 11))
>>> 19.99999999999992894573

Upvotes: 0

Adib Saad
Adib Saad

Reputation: 572

11.2 - 11

actually yields

0.1999999999999993

which rounds down to 19.

Upvotes: 4

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