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.


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!

Enjoy this page? Please pay it forward. Here's how...

Would you prefer to share this page with others by linking to it?

  1. Click on the HTML link code below.
  2. Copy and paste it, adding a note of your own, into your blog, a Web page, forums, a blog comment, your Facebook account, or anywhere that someone would find this page valuable.
Share this page: