Rational Numbers vs Irrational Numbers — Difference (with Table & FAQs)
Rational and irrational numbers complete the real number system, essential for CBSE Class 9 Mathematics. Understanding their differences is fundamental to
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TL;DR: Rational and irrational numbers complete the real number system, essential for CBSE Class 9 Mathematics. Understanding their differences is fundamenta…
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The main difference between Rational Numbers and Irrational Numbers: Rational and irrational numbers complete the real number system, essential for CBSE Class 9 Mathematics. Understanding their differences is fundamental to
Rational Numbers vs Irrational Numbers — Comparison Table
| Basis | Rational Numbers | Irrational Numbers |
|---|---|---|
| Definition | Can be expressed as p/q (p,q integers, q≠0) | Cannot be expressed as fraction of integers |
| Decimal form | Terminating or repeating decimal | Non-terminating, non-repeating decimal |
| Examples | 1/2, 3/4, 0.5, 0.333... | √2, √3, π, e |
| Density on number line | Infinite but countable | Infinite and uncountable |
| Can be written as integer ratio | Yes | No |
Key Points
- Rational = p/q where p and q are integers; irrational cannot be expressed as simple fraction
- Repeating decimals are rational (0.333... = 1/3); non-repeating are irrational (π = 3.14159...)
- √2 is irrational because it cannot be expressed as fraction of two integers
- Between any two rational numbers, infinite irrational numbers exist