12 replies to this topic

[1984]

hmmm.

[krit86lr]

Lordoftheweb, on Mar 13 2006, 06:54 PM, said:

hmmm.

Are you really asking for an answer?
76%

[1984]

exactly 76% or a little bit less than, or a little bit more than? and how did you figure it out. exactly.

oh, and thanks babe.

[krit86lr]

Lordoftheweb, on Mar 13 2006, 07:32 PM, said:

exactly 76% or a little bit less than, or a little bit more than? and how did you figure it out. exactly.

oh, and thanks babe.

You're silly...

This is what you do:
1. Divide 26.5 by 35. (visual 26.5/35)
2. The result is 0.7571......
3. You multipy the result by 100. (visual 0.7571 X 100)
3. The result is 75.71%.
4. Because the answer is equal to or greater than 75.5 the answer gets rounded up to 76%!

You're welcome babe.

[1984]

thanks again! thats what i thought, but my brain doesnt seem to be working today. i just cant seem to get numbers in order.

[krit86lr]

I've been there.

Glad that I could explain it okay. I'm better at getting answers than explaining how I get them.

[Andavari]

What about rounding errors? Since digital after all has rounding errors.

[krit86lr]

Andavari, on Mar 13 2006, 09:04 PM, said:

What about rounding errors? Since digital after all has rounding errors.

What do you mean by rounding errors? That it isn't the exact number? As in pie being referred to as 3.14 rather than the 56 or so decimal places?

[lokoike]

Andavari, on Mar 13 2006, 09:04 PM, said:

What about rounding errors? Since digital after all has rounding errors.

Rounding "errors"? What is erroneous about digital rounding?

Computers perform math the same way that we do, except they use binary as opposed to decimal. Computers don't always truncate numbers, if that is what you mean by a "rounding error". They round the same way you would: > 4 = round up & < 5 = round down. You can digitally simulate any form of rounding, whether it be normal rounding, truncating, significant figures, whatever.

Anything analogous can be recreated digitally. At least, I personally can't think of any exceptions.

[Andavari]

It's beyond difficult to explain, so here's a Google search to more than a plethora of references. And a Wikipedia reference.

[lokoike]

Andavari, on Mar 14 2006, 03:56 AM, said:

It's beyond difficult to explain, so here's a Google search to more than a plethora of references. And a Wikipedia reference.

Oh, I see what you mean. Although, I believe that those errors only occur if you set up the item like an equation. That is something I noticed on my TI-86 graphing calculator a long time ago. If you use the in-calculator equation solver, and a problem is supposed to equal zero, it might end up equaling 0.00000000000001, or something silly like that. But I found that if you put in 0 as the possible solution, then it would realize that that was the correct answer, and it wouldn't give you an approximation.

So if you used a computer and entered in:

(26.5*100)/35

you would get the correct answer.

But, if you used that same computer, and set it up as an equation:

26.5/35=x/100

then you might potentially get rounding errors.

At least, this is my understanding. My programming knowledge is pretty much limited to BASIC...

[Glenn]

Although it's not a problem for most, theoretically, any calculation involving decimals or fractions is subject to rounding errors. The decimal input has to be converted to binary for processing (possibly multiple stages) and then converted back to decimal output.

The processor has to pick a "best fit" conversion at each stage. The limits of precision have improved with each generation of processor but, in the old days, you would regularly see discrepancies if you went to enough decimal places. I seem to recall there was an entire model of early Pentium's recalled because of unacceptable rounding errors.

[lokoike]

Glenn, on Mar 15 2006, 09:15 AM, said:

Although it's not a problem for most, theoretically, any calculation involving decimals or fractions is subject to rounding errors. The decimal input has to be converted to binary for processing (possibly multiple stages) and then converted back to decimal output.

The processor has to pick a "best fit" conversion at each stage. The limits of precision have improved with each generation of processor but, in the old days, you would regularly see discrepancies if you went to enough decimal places. I seem to recall there was an entire model of early Pentium's recalled because of unacceptable rounding errors.

Okay, that helps clarify it. Thanks guys.

And the fact that it was Intel procs that had to be recalled doesn't surprise me in the least.