Dividing a float by 10

Question

Possible Duplicate:
Why can't decimal numbers be represented exactly in binary?

I am developing a pretty simple algorithm for mathematics use under C++.

And I have a floating point variable named "step", each time I finish a while loop, I need step to be divided by 10.

So my code is kind of like this,

float step = 1;
while ( ... ){
      //the codes
      step /= 10;
}

In my stupid simple logic, that ends of well. step will be divided by 10, from 1 to 0.1, from 0.1 to 0.01.

But it didn't, instead something like 0.100000000001 appears. And I was like "What The Hell"

Can someone please help me with this. It's probably something about the data type itself that I don't fully understand. So if someone could explain further, it'll be appreciated.

You should also read: [What Every Computer Scientist Should Know About Floating-Point Arithmetic](http://docs.oracle.com/cd/E19957-01/806-3568/ncg_goldberg.html). — AusCBloke, Dec 24 '11 at 06:35
Shane: Please do not retype content here. Copy and paste. People get very frustrated and downvotey when they find they've spent fifteen minutes debugging a problem that never existed. (Well, _I_ get frustrated and downvotey. Others might react better.) — sarnold, Dec 24 '11 at 06:36
You could divide by 2 (or 8) instead if that's an option, which will give you somewhat more accurate values. — Kerrek SB, Dec 24 '11 at 15:50

score 5 · Accepted Answer · answered Dec 24 '11 at 06:26

5

It is a numerical issue. The Problem is that 1/10 is a endless long number in binary and the successive apply of a division by 10 ends up with summing the error in each step. To get a more stable version you should multiply the divisor. But take care: the result is also not exact! You may want to replace the float with a double to minimize the error.

unsigned int div = 1;
while(...)
{
    double step = 1.0 / (double)div;
    ....
    div *= 10;
}

answered Dec 24 '11 at 06:26

thomas

5,637
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`div` should probably also be a floating point type, or you won't get very far with this. – Kerrek SB Dec 24 '11 at 15:49

score 2 · Answer 2 · answered Dec 24 '11 at 06:20

The division by ten cannot be exact for binary floating point arithmetic, so you see results that will look a little bit off from what you expect.

Binary floating are represented as an integer ratio where the denominator is a power of two. Since there in no binary fraction exactly equal to one-tenth, you'll see the nearest representable number instead of the one you expected.

Dividing a float by 10

2 Answers2