Base

Type: definition

In base $b$, a number
\[
  A=a_n\ldots a_1a_0
\]
equals
\[
  A=\sum_{i=0}^{n} a_i b^i.
\]

A decimal
\[
  A=0.a_1a_2\ldots a_n
\]
equals
\[
  A=\sum_{i=1}^{n} a_i b^{-i}.
\]

Essentially, shifting digits multiplies by $b$ or $\frac{1}{b}$.