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

PDF chapter test TRY NOW

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: