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    zacho7805's Avatar
    zacho7805 Posts: 1, Reputation: 1
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    #1

    May 3, 2009, 10:44 PM
    a terminating decimal
    does there exist a fraction, which is in lowest terms, x/y such that in which y>x and

    x/y=.abcabcabcd s.t. 1≤a≤8
    5≤b≤9
    0≤c≤9
    d=a+1
    ebaines's Avatar
    ebaines Posts: 12,131, Reputation: 1307
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    #2

    May 4, 2009, 08:59 AM

    Zacho - perhaps I don't quite understand what you're getting at, but if you pick any values you want for a,b,c, and d that satisfy your constraints you have a decimal of fixed length, and any decimal of fixed length can always be expressed as a fraction. For example, suppose you set a=4, b=6, c=2: then d = 5 and you have:

    x/y = .4624624625
    So x = 4,624,624,625and y = 10,000,000,000

    This can be reduced to a proper fraction with no common factors between the numerator and denominator - in his case you can divide top and bottom by 125 to get:
    36,996,997/80,000,000
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