# nLab decimal rational number

### Context

#### Algebra

higher algebra

universal algebra

# Contents

## Definition

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

1. the decimal expansion of $r$ has finitely many digits;

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

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