# What is the reason of inaccuracy of operations on float numbers?

I wonder why in JavaScript

0.1 + 0.2  // return 0.30000000000000004

4%0.1 // return 0.09999999999999978


http://jsbin.com/oHISAfU/1/edit (Example)

In C the math.h library fmod function

printf("%f", fmod(4.0,0.1));  // print 0.100000


http://ideone.com/RG5Wyv (Example)

And in Spotlight (search feature in the Mac OS X ~ I already submit bug report) that support math operation

4%0.1 = 0.1


 printf("%.20f", fmod(4.0,0.1));

prints 0.09999999999999978351.
Ilmari Karonen gets it right in the other answer. But it gets even worse than that: arithmetic operations involving floating-point numbers don't necessarily behave the same as operators we're used to from mathematics. For instance, we're used to addition being associative, so that $a + (b + c) = (a + b) + c$. This doesn't generally hold using floating-point numbers, and for a given format it's not hard to come up with counterexamples. Not exactly relevant to the question you asked, except to illustrate that you should never assume floating point calculations are going to be exact.
• In particular, for sufficiently large $a$ and sufficiently small $b > 0$, it's quite possible that $a + b = a$ in floating point. – Ilmari Karonen Aug 19 '13 at 18:56