Decimal expansion of irrational number — lesson. Mathematics State Board, Class 9.

UPSKILL MATH PLUS

Learn Mathematics through our AI based learning portal with the support of our Academic Experts!

The decimal expansion of an irrational number is non-terminating and non-recurring. Conversely, the decimal expansion of a number is non-terminating and non-recurring is an irrational number.

Example:

Many square roots and cube roots are irrational numbers.

Let us find the square root of

\sqrt{5}

Thus, the decimal expansion of

\sqrt{5}

have non-terminating and non-recurring decimals.

It goes like

\sqrt{5} = 2.2360...

\begin{array}{l} \sqrt{3} = 1.7320508075... \\ \sqrt{5} = 2.2360679774... \\ \sqrt[3]{3} = 1.4422495707... \end{array}

Some of the famous irrational numbers:

Irrational Number	Its non-terminating and non-recurring decimal value
$π (pi)$	$3.141592653589793$...
$e (Eulers number)$	$2.718281828459045$...
$ϕ (Golden ratio)$	$1.618033988749894$...

Previous theory

Exit to the topic

Next theory

Send feedback

Did you find an error?

Send it to us!

6. Decimal expansion of irrational number

Theory: