Question

Which among the following is irrational?

• A. 0.2
• B. 3.1415926535... (non-repeating and non-terminating)
• C. $\frac{1}{0.2}$
• D. $(0.2{)}^2$

Answer 1

The correct option is B

3.1415926535... (non-repeating and non-terminating)

Non-terminating and non-repeating decimals are irrational.

If the denominator of a rational number is in the form of $2^n{5}^m$ where n and m are non-negative integers, then the rational number is terminating.

$0.2=\frac{2}{10}=\frac{2}{2\times 5}$

$\therefore$ 0.2 has terminating decimal and is a rational number.

3.1415926535... is non-terminating and non-repeating.

$\therefore$ 3.1415926535... is irrational.

$\frac{1}{0.2}=\frac{10}{2}$

$\therefore$ $\frac{1}{0.2}$ has terminating decimal and is a rational number.

$(0.2{)}^2=(\frac{0.2}{10}{)}^2=(\frac{0.2}{2\times 5}{)}^2$

$(0.2{)}^2$ has terminating decimal and is a rational number.