Rational and Irrational Numbers | Mathematics
As you know, the word rational means “logical” and the word irrational means “illogical.” Similarly, numbers hold the same definitions. Understanding and recognizing rational and irrational numbers is a high emphasis topic on the TASC Test Assessing Secondary Completion™ Mathematics subtest.
Let’s dive in and analyze each of these terms individually.
According to MathWarehouse.com, a rational number is any number that can be written as a fraction with a denominator greater than zero.
Study these examples of rational numbers:
- 19 can be written as: 19⁄1
- -32 can be written as: -32⁄1
- .75 can be written as: 3⁄4
- √9 (square root) = 3 which can be written as: 3⁄1
Rational numbers have either a limited number of decimals (such as = 0.75) or a repeating number of sequenced decimals (such as = 0.333333333…). It is important to note that repeating decimals – decimals that repeat the same sequence of digits indefinitely – are rational numbers.
- .125125125125… repeats in a sequence of 125
- .333333333333… repeats in a sequence of 3
Irrational numbers are numbers that cannot be written as a fraction with a denominator greater than zero.
Study these examples of irrational numbers:
- √11 cannot be simplified into a fraction like √9
- π (pi = 3.14159265359…) cannot be simplified into a fraction
- .0303003000030330… cannot be simplified into a fraction
- has a denominator of zero
Numbers that repeat indefinitely with non-repeating digits are irrational numbers, as seen in the example of .0303003000030330…
Test your knowledge of rational and irrational numbers by quizzing yourself at KhanAcademy.org.