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?
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Submitted by Gamer
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Rating: 3.0000 (5 votes)
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Solution:
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13,717,421 and 1,111,111,111
Using the rule that to get a repeating decimal, you divide the number by as many 9s as digits in the number, you do:
0,123,456,789/9,999,999,999
Since the leading zero counts as a decimal place, it needs to be included in the count. But since both these numbers have a factor of 9, this must be divided out.
This leaves 13,717,421 and 1,111,111,111 and because 13,717,421 is equal to 3607 x 3803 and 1,111,111,111 is equal to 11 x 41 x 271 x 9091, these numbers are relatively prime. |
