odd one out

[scampibubble]

Which is the odd one out and why?

40/104, 60/140, 75/170, 90/194

Cheers

[jake-the-peg]

90/194 is 0.46391752577319587628865979381443.. it appears to be irrational.

An irrational number expressed as a decimal does not repeat or terminate like 40/104 0.38461538461538461538461538461538...

60/140 0.42857142857142857142857142857143..

or 75/170 0.44117647058823529411764705882353

However by definition an irrational number cannot be expressed as two integers p and q one divided by another (p/q) so 90/194 cannot be truely irrational, presumably the sequence is just too long to repeat on a normal calculator.

see here for more information on irrational numbers:

http://mathworld.wolfram.com/IrrationalNumber.html

[jake-the-peg]

actually 90/194 is

0.46391752577319587628865979381443298969072164948453608247422680412371134020618556701030927835051546
3917525773195876288659793814432989690721649484536082474226804123711340206185567010309278350515463917
53

you can use this site to calculate with arbitary precision

http://www.cs.indiana.edu/~flaradam/applications/Calcula tor/CalBig/ts/SC.html