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# Difference between Rational and Irrational Numbers

May 7, 2023 written by Azhar Ejaz

The key difference between rational and irrational numbers is that rational numbers can be expressed as a ratio of two integers, while irrational numbers cannot be expressed as simple fractions.

## 5 Differences between Rational and Irrational Numbers

1. Rational numbers can be expressed as simple fractions, while irrational numbers cannot be expressed in simple fractions.
2. Rational numbers have a finite or repeating decimal representation, while irrational numbers have an infinite non-repeating decimal representation.
3. Rational numbers are closed under addition, subtraction, multiplication, and division, while irrational numbers are not.
4. The sum, difference, product, and quotient of rational numbers are always rational, while the sum, difference, product, and quotient of irrational numbers can be either rational or irrational.
5. Examples of rational numbers include 2/3, 5/4, 0.25 (1/4 in decimal form), and 0.6 (3/5 in decimal form). Examples of irrational numbers include √2 (the square root of 2), π (pi), e (Euler’s number), and φ (the golden ratio).
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