How do irrational numbers differ from rational numbers?

1 Answer
George C.
Mar 29, 2016

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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