[wjvipqnk] Base 9.x or 10-epsilon

Pick a fractional base between 9 and 10: 9 < base < 10.  A number written in that base looks like it's in base 10 decimal (because it uses the digits 0 through 9) but isn't.  For example 1/2 written in base 9.5 is 0.471174006660144931361358614588...  Here is some PARI/gp code:

? \p1000
? base=9.5;x=0.5;for(i=1,30,x=x*base;d=floor(x);print1(d);x=x-d)

Many (most) ordinary fractions look irrational.

You might be able to tell it's not base 10 because the digit 9 occurs less frequently than expected.  However, this could be concealed by choosing a base very close to 10.  For example, 1/2 in base 9.999 is 0.499938912222668420772584737231 . It approximates 0.5000 for as many nines there are in the base after the decimal point.  There are some patterns that persist longer, but eventually it looks random.  1/2 in base 9.999999999 = 0.499999999938888888948888888818500000115688888699835555883178666063808640026415359006307736218805374454874664379695541795287272213500649931128973335432...

Consider chopping off the prefix that looks nonrandom to conceal that it was a rational number.  If you know the base, computing the continued fraction on the remaining digits might be useful to recover the original fraction or something like it.  Not sure what this might be useful for.