Rational vs Irrational Numbers
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Examples, videos, worksheets, and solutions to help Grade 8 students learn about rational numbers and irrational numbers.
A rational number is a number that can be written as a fraction whose numerator and denominator are both integers (and the denominator must not be zero). An irrational number is a number that cannot be expressed as a finite or repeating decimal.
Rational Numbers
Definition: A rational number is any number that can be expressed as a fraction \( \frac{p}{q} \) where \( p \) and \( q \) are integers but \( q \) ≠ zero. The word “rational” comes from the word “ratio”.
Decimal Representation: When a rational number is expressed as a decimal, it either:
Terminates: The decimal ends after a finite number of digits (e.g., \( \frac{1}{4} \) = 0.25)
Repeats: The decimal has a sequence of digits that repeats infinitely (e.g., \( \frac{1}{3} \) = 0.333…)
The following diagram gives some properties and examples of rational numbers and irrational numbers. Scroll down the page for more examples and solutions.
Fraction, Decimal & Rational Number Worksheets
Practice your skills with the following worksheets:
Online & Printable Fraction Worksheets
Online & Printable Decimal Worksheets
Online & Printable Rational Number Worksheets
Irrational Numbers
Definition: An irrational number is a real number that cannot be expressed as a fraction \( \frac{p}{q} \) where \( p \) and \( q \) are integers but \( q \) ≠ zero.
Decimal Representation: When an irrational number is expressed as a decimal, it is non-terminating and non-repeating. The decimal goes on forever without any pattern of digits repeating.
Examples:
\( \sqrt(2) \) ≈ 1.414213…
π ≈ 3.14159…
Square roots of non-perfect squares (e.g., \( \sqrt{5} \), \( \sqrt{6} \), etc.)
Cube roots of non-perfect cubes (e.g., \( \sqrt[3]{2} \), \( \sqrt[3]{3} \), etc.)
Rational vs. Irrational Numbers
This video explains the difference between rational and irrational numbers and how to identify rational and irrational numbers.
Rational and Irrational Numbers
Irrational Numbers
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