Definition:Decimal Expansion

Definition
Let $x \in \R$ be a real number.

The decimal expansion of $x$ is the expansion of $x$ in base $10$.

$x = \floor x + \displaystyle \sum_{j \mathop \ge 1} \frac {d_j} {10^j}$:
 * $\sqbrk {s \cdotp d_1 d_2 d_3 \ldots}_{10}$

where:
 * $s = \floor x$, the floor of $x$
 * it is not the case that there exists $m \in \N$ such that $d_M = 9$ for all $M \ge m$.

(That is, the sequence of digits does not end with an infinite sequence of $9$s.)

Also see

 * Definition:Continued Fraction Expansion of Real Number