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Minor Problem
Authored by: alexiskai on Oct 09, '02 10:17:45AM

Remember that this is only true for extremely large values of .07. ;)



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Minor Problem
Authored by: BigEndian on Oct 09, '02 10:48:14AM

I suspect this has to do with binary to decimal conversion.

When you enter a decimal number (such as 0.07) into the calculator it must convert it to binary (such as 1001101) so it can be used by the processor. Some numbers that are rational in decimal are irrational in binary (an irrational number is one that goes forever, like 1/3 = 0.3333333...).

What this means, is that the calculator is most likely doing the calculation properly (which are done in binary) and is only adding a very small error when it converts to and from binary.

BTW, most calculators work the same way except they round off so you never see the final digit (ie 0.07000000000001 = 0.7)

That's just my opinion, I could be worng...



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Minor Problem
Authored by: j-beda on Oct 09, '02 10:56:33AM

Actually, a number is rational if it can be expressed as p/q with both p
and q being integers. Thus 1/3 is rational, and it is still rational when expressed as a decimal 0.33333... Rational numbers expressed as a decimal repeat a patern such as 0.33333... and 0.50000... (sometimes that patern is a bunch of repeating zeros which are usually not written).

Irrational numbers such as pi, e and the square root of 2 cannot be so expressed either as a repeating decimal or as p/q.



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Minor Problem
Authored by: j-beda on Oct 09, '02 10:58:29AM

Hey! Where did the comment I was replying to go? Someone had commented that 1/3 was irrational when expressed as a decimal...



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Right concept - wrong name
Authored by: avonterr on Oct 09, '02 02:38:51PM

It's not that 0.7 isn't "rational" in base-2, it's that it "doesn't have a finite base-2 expansion." As far as I know, there isn't a widely used one-name word for this category.



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