How do irrational numbers differ from rational numbers?

Question

Everly Taylor · Accepted Answer

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

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)#. A number's decimal expansion won't end or repeat if it is irrational. As an illustration, #pi = 3.141592653589793238462643383279502884...#

Emery Allen · Answer

undefined Irrational numbers cannot be expressed as the ratio of two integers, while rational numbers can. Rational numbers can be written in the form a/b, where a and b are integers and b is not equal to zero. Irrational numbers cannot be expressed as a fraction of two integers and cannot be represented as terminating or repeating decimals. Irrational numbers are non-repeating and non-terminating decimals. Additionally, irrational numbers cannot be expressed as fractions, and they possess an infinite number of non-repeating digits after the decimal point.

Noah Archer · Answer

undefined Irrational numbers cannot be expressed as a fraction of two integers. They have non-repeating, non-terminating decimal expansions. Rational numbers, on the other hand, can be expressed as fractions of two integers. They have either terminating or repeating decimal expansions. Additionally, rational numbers include integers and fractions.