Difference Between Rational and Irrational Numbers
Rational number A rational number (Q) is any number which can be written as: a/b. While Irrational numbers (Q′ ) are numbers that cannot be written as a fraction with the numerator and denominator as integers. Here's a simple comparison to understand their differences:
| Rational Numbers | Irrational Numbers |
|---|---|
| Can be expressed as a fraction (p/q) where q ≠ 0 | Cannot be expressed as a simple fraction |
| Decimal representation either terminates or repeats | Decimal representation goes on forever without repeating |
| Examples: 1/2, 0.75, -3, 4.333… | Examples: √2, π (pi), e |
| Includes integers and fractions | Excludes all integers and proper fractions |
| Countable set | Uncountable set |
Note: Both rational and irrational numbers are part of the real number system.
Take Online Quiz: Mathematics Quiz
Exercise: Identify Rational and Irrational Numbers
Classify each of the following numbers as Rational or Irrational:
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1) 3.14159
2) 5/8
3) √5
4) 7
5) 0.333…
6) √16
7) π (pi)
8) 2.5
9) 1.01001000100001…
10) 22/7
Instructions: Write "Rational" or "Irrational" next to each number. Justify your answers if needed.
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