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
Try out our new and fun Fraction Concoction Game.
Add and subtract fractions to make exciting fraction concoctions following a recipe. There are four levels of difficulty: Easy, medium, hard and insane. Practice the basics of fraction addition and subtraction or challenge yourself with the insane level.
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