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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…

Written & reviewed by the Syllab.in Academic Team (CBSE/NCERT subject experts) · Updated Jul 23, 2026

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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

BasisRational NumbersIrrational Numbers
DefinitionCan be expressed as p/q (p,q integers, q≠0)Cannot be expressed as fraction of integers
Decimal formTerminating or repeating decimalNon-terminating, non-repeating decimal
Examples1/2, 3/4, 0.5, 0.333...√2, √3, π, e
Density on number lineInfinite but countableInfinite and uncountable
Can be written as integer ratioYesNo

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

More Maths Comparisons

  • Difference Between Prime and Composite Numbers
  • Difference Between Area and Perimeter
  • Difference Between Square and Rectangle
  • Difference Between Square and Rhombus
  • Difference Between Mean and Median
  • Difference Between Permutation and Combination

See all difference-between comparisons →

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