Decimal expansion of irrational — lesson. Mathematics CBSE, Class 9.

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

\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
$π (pi)$	$3.141592653589793$...
$e (Eulers number)$	$2.718281828459045$...
$ϕ (Golden ratio)$	$1.618033988749894$...

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7. Decimal expansion of irrational

Theory: