IRRATIONAL NUMBERS
Irrational numbers are the set of real numbers that cannot be expressed in the form of a fraction, p/q where p and q are integers. The denominator q is not equal to zero (q ≠ 0). Also, the decimal expansion of an irrational number is neither terminating nor repeating.
Examples of Irrational Numbers
- ㄫ(pi) is an irrational number. π=3⋅14159265… The decimal value never stops at any point. Since the value of ㄫ is closer to the fraction 22/7, we take the value of pi as 22/7 or 3.14 (Note: 22/7 is a rational number.)
- √2 is an irrational number. Consider a right-angled isosceles triangle, with the two equal sides AB and BC of length 1 unit. By the Pythagoras theorem, the hypotenuse AC will be √2. √2=1⋅414213⋅⋅⋅⋅
- Euler’s number e is an irrational number. e=2⋅718281⋅⋅⋅⋅
- Golden ratio, φ 1.61803398874989….
