Question

Write three numbers whose decimal expansions are non-terminating non-recurring.

Answer 1

Three numbers whose decimal expansions are non-terminating and non-recurring are:
i) $\mathrm{0.123123312333...}$
ii) $\mathrm{0.20200200020000...}$
iii) $\mathrm{0.56566566656666...}$

Here, the expansion goes on without terminating and though the decimal part follows a definite pattern, no block of digits are repeating, i.e. non-recurring.

NOTE:

1. Any irrational number has non-terminating non-recurring decimal expansions.

For example, $\sqrt{2}$, $\sqrt{3}$, $\sqrt{5}$. etc.

2. The numbers which cannot be written in $\frac{p}{q}$ form are known as irrational numbers.

3. If the natural number $n$ is not a square number, then the square root of $n$, i.e. $\sqrt{n}$ is an irrational number.