# Base-b expansion of a number?

1. ### iceblits

113
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. ### iceblits

113
Oh it's just referring to writing a number in a different base...

3. ### Bacle2

1,168
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