Tuesday, August 09, 2011

[prjwxpih] Worst decimal fraction

The number 4/9 = 0.444... when rounded to any number of decimal digits, has a 4 rounded down to a 0, for an error that always looks like 0.000...444... 4 is pretty big on a scale that goes from 0 to 5.

The number 5/9 = 0.555... has the same error, with the 5 rounded up.

The number 5/11 = 0.454545... has slightly higher constant error, always looking like 454545... regardless of whether you round to an even or odd number of decimal digits.

Similarly 6/11 = 0.545454...

Is there a number with worse error?  I'm guessing not.  The denominators are 9 and 11 which surround base 10.

I wonder if these rounding characteristics can be used for nefarious purposes: "Buy 11 for a dollar!"

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