I was using a calculator one day, and punched in a number, then punched "divided by", then punched another number and got back .01234567890123456789... I thought the calculator was wacko, but the calculator was right.

If the two numbers I put in were relatively prime, what were they?

Any decimal fraction which begins repeating right after the decimal point is the repeated set of digits treated as an integer over an integer formed from as many 9's as are in the repetition period. So .01234567890123456789... is 123456789/9999999999 (that's 10 9's in the denominator as the period is 10). The two numbers have 9 as their highest common factor and so the fraction reduces to 13717421/1111111111, where the numerator and denominator are relatively prime.

Posted by Charlie on 2003-07-03 02:57:15