For each k>1 compute the k-ary expansion of 1/2. This is for a proofs course so please so all work, and I already know the answer just not sure how to explain it. Thanks Solution Base 2: 0.1 Base 4: 0.2 Base 6: 0.3 Base 8: 0.4 Base 10: 0.5 (we already knew that one) Well I think you get the idea for even bases ... for base b, let h = half the base or b/2. 1/2 (base 10) = 0.h (base b) Odd bases are a little trickier. We want an infinite series of fractions which sum to 1/2, with each denominator a power of an integer. You can do long division in the given base until the remainder is a repeat: 2 into 1 base 3: (all numbers in base 3) 2 into 10 goes 1 time, remainder 1 ... well that was quick: it\'s 0.111111111111... (repeating infinitely) 2 into 1 base 5: That one was just as fast, since 5 = 2*2 + remainder 1 it\'s 0.22222222222... Well, it will be like that for all of them, won\'t it ? since every odd base leaves remainder 1 when divided by 2. Base 7: .333333333333... Base 9: .4444444444444... Base 11: .5555555555555... Let h = (base - 1) / 2 for odd base. Then you have 0.hhhhhhhh... repeating (base b) = 1/2 (base 10). Source(s): Here is a page with a general algorithm for converting any fraction from decimal to another base: http://www.cut-the-knot.org/blue/frac_conv.shtml.