Irrational number

An irrational number is a number that cannot be expressed in the form a/b, where a and b are integers. For example, 0.3333333 = 1/3, where 1 and 3 are integers. Therefore, 0.333333 can be expressed as a rational number.

However, it is not possible to find any integers a and b such as 3.3166247 = a/b. Therefore, 3.3166247 is an irrational number since it cannot be expressed as a rational number.

More examples of irrational numbers

The number Pi: π = 3.14159265358979323846

Euler's Number: e = 2.71828182845904523536028

The Golden Ratio: φ = 1.618033988749894848

The square root of {2, 3, 5, 6, 7, 8, 10, 12, 13, ....}


A number may look irrational and yet be a rational number.

For example, 0.245610245610245610 looks irrational. However, it is a rational number!

in fact, 0.245610245610245610 = 27290/111111


How did you get mixed up? Numbers that have a single number or a group of numbers that repeats are not irrational.

0.245610245610245610

Notice how 245610 is a group of numbers that repeat itself.

Finally, in a/b, b cannot be a power of 10. for example, you cannot say that π = 3.14159 = 314159/100000 is a rational number!

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