nLab
decimal rational number

Contents

Context

Arithmetic

Algebra

Contents

Definition

A decimal rational number or decimal fraction is a rational number rr \in \mathbb{Q} such that the following equivalent conditions hold

  1. the decimal expansion of rr has finitely many digits;

  2. there exists n,an,a \in \mathbb{N} such that r=a10 nr = \frac{a}{10^n}.

The commutative ring of decimal rational numbers [1/10]\mathbb{Z}[1/10] is the localization of the integers \mathbb{Z} away from 1010.

References

Last revised on May 8, 2021 at 21:17:20. See the history of this page for a list of all contributions to it.