The main difference between rational and irrational numbers lies in their ability to be expressed as a fraction.
Rational Numbers
A rational number is any number that can be written as a fraction, where the numerator and denominator are both integers, and the denominator is not zero.
Examples of rational numbers include:
- 1/2
- 3 (can be written as 3/1)
- -4/5
- 0.75 (can be written as 3/4)
Rational numbers can be represented on a number line, and they have a finite or repeating decimal representation.
Irrational Numbers
An irrational number cannot be expressed as a simple fraction of two integers.
Examples of irrational numbers include:
- π (pi) - the ratio of a circle's circumference to its diameter
- √2 (the square root of 2)
- e (Euler's number) - the base of the natural logarithm
Irrational numbers have an infinite and non-repeating decimal representation. This means their decimal representation goes on forever without any repeating patterns.
Summary
In summary, the key difference between rational and irrational numbers is their ability to be expressed as a fraction. Rational numbers can be written as a fraction, while irrational numbers cannot.
