Question

How do irrational numbers differ from rational numbers?

Answer 1

Rational numbers can be expressed as fractions, irrational numbers cannot...

Explanation:

Rational numbers can be expressed in the form `p/q` for some integers `p` and `q` (with `q != 0`). Note that this includes integers, since for any integer `n = n/1`.

For example, `5`, `1/2`, `17/3` and `-7/2` are all rational numbers.

Any other Real number is called irrational. For example `sqrt(2)`, `pi`, `e` are all irrational numbers.

If a number `x` is rational, then its decimal expansion will either terminate or repeat.

For example, `213/7 = 30.428571428571...`, which we can write as `30.bar(428157)`.

If a number is irrational, then its decimal expansion will neither terminate nor repeat. For example,

`pi = 3.141592653589793238462643383279502884...`