Kĩnũthia Mũchane wrote:
On 06/12/2011 08:13 PM, Steven D'Aprano wrote:
Unfortunately, many common fractions cannot be written exactly in
binary. You're probably familiar with the fact that fractions like 1/3
cannot be written exactly in decimal:
1/3 = 0.33333333... goes on forever
Does it? :-)
Yes.
0.3 is not 1/3, it is 3/10, not 3/9.
0.33 is not 1/3, it is 33/100, not 33/99.
0.333 is not 1/3, it is 333/1000, not 333/999.
...
0.3333333333 is not 1/3, it is 3333333333/10000000000 instead of
3333333333/9999999999.
And so forth. No matter how many 3s you have, it will always be just
short of 1/3. Anything less than an infinite number of decimal places is
not 1/3 exactly, but some approximation less than 1/3.
--
Steven
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