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Baseb expansion of a number? 
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#1
Feb2812, 07:04 PM

P: 113

Has anyone come across how to find "the baseb expansion" of a number? I don't think its tricky or anything I just don't know what it's referring to...



#2
Feb2812, 07:07 PM

P: 113

Oh it's just referring to writing a number in a different base...



#3
Mar112, 08:02 PM

Sci Advisor
P: 1,172

(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_{(m1)}.c+ b_{(m2)}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. 


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