How do irrational numbers differ from rational numbers?

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How do irrational numbers differ from rational numbers?

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Answer 1 · 2016-03-29T19:39:52

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,

$pi = 3.141592653589793238462643383279502884...$

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How do irrational numbers differ from rational numbers?

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