Base-b expansion of a number?

  1. 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...
     
  2. jcsd
  3. Oh it's just referring to writing a number in a different base...
     
  4. Bacle2

    Bacle2 1,175
    Science Advisor

    AFAIK, expressing a number in base c it refers to expressing a number, usually given in base 10-- in the form:

    (b0b1...bm.b(m+1)....b(m+k))c

    (let's assume for simplicity the decimal expansion is finite)

    Which represents the expression:

    1)Whole Part: bm+b(m-1).c+ b(m-2)c2+

    ....+bmcm

    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:

    0.20+1.21+1.22=21+22=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 3.100+1.101 in the

    whole part, and 2.10-1 in the4 decimal part.
     
    Last edited: Mar 1, 2012
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