Has anyone come across how to find "the base-b expansion" of a number? I don't think its tricky or anything I just don't know what it's referring to...
AFAIK, expressing a number in base c it refers to expressing a number, usually given in base 10-- in the form: (b_{0}b_{1}...b_{m}.b_{(m+1)}....b_{(m+k)})_{c} (let's assume for simplicity the decimal expansion is finite) Which represents the expression: 1)Whole Part: b_{m}+b_{(m-1)}.c+ b_{(m-2)}c^{2}+ ....+b_{m}c^{m} 2)Decimal Part: b_{(m+1)}c^{-1}+b_{(m+2)}c^{-2}+ ...+b_{(m+k)}c^{-k}+....... An example I think most would be familiar with would be a binary string, say: (110.0101)_{2} Which stands for: 1')Whole Part: 0.2^{0}+1.2^{1}+1.2^{2}=2^{1}+2^{2}=6 2')Decimal Part: 0.2^{-1}+1.2^{-2}+0.2^{-3}+1.2^{-4}= 1/4+1/16=5/16 So the string 110.0101 Represents , in base 2, the number 6.325 in base 10. Or, like (13.2)_{10} represents 3.10^{0}+1.10^{1} in the whole part, and 2.10^{-1} in the4 decimal part.