Rational numbers

A rational number is any number that can be written as a fraction of two integers.

By definition, all rational numbers are also real numbers.

Notation

The set of rational numbers is usually denoted by the symbol \mathbb{Q}:

\mathbb{Q} = \left\{ \frac{a}{b} \mid a, b \in \mathbb{Z}, b \neq 0 \right\}

\frac{1}{2}
-3 (can be written as \frac{-3}{1})
0 (can be written as \frac{0}{1})
4.75 (can be written as \frac{19}{4})
-0.1 (can be written as \frac{-1}{10})
3.333\ldots (can be written as \frac{10}{3})
7 (can be written as \frac{7}{1})

Question	Answer
What is a rational number?	A rational number is any number that can be written as a fraction of two integers.
How are rational numbers related to real numbers?	By definition, all rational numbers are also real numbers.
What symbol denotes the set of rational numbers?	\mathbb{Q}
Write the set-builder notation for rational numbers.	\mathbb{Q} = \left\{ \frac{a}{b} \mid a, b \in \mathbb{Z}, b \neq 0 \right\}
Is -3 a rational number? Why?	Yes, because it can be written as \frac{-3}{1}, a fraction of two integers.
Is 4.75 a rational number? Why?	Yes, because it can be written as \frac{19}{4}, a fraction of two integers.
Is 3.333\ldots a rational number? Why?	Yes, because it can be written as \frac{10}{3}, a fraction of two integers.
Is 0 a rational number? Why?	Yes, because it can be written as \frac{0}{1}, a fraction of two integers.
Why is \sqrt{2} not a rational number?	It is irrational.
Why is \pi not a rational number?	It is irrational.
Why is e not a rational number?	It is irrational.
Why is i not a rational number?	It is not a real number.