Question

Which of the following is/are an irrational number?

• A. $1.2$
• B. $\mathrm{0.3030030003...}$
• C. $\mathrm{1.4151617...}$
• D. $\sqrt{4}$

Answer 1

Answer: (B), (C)

$\mathrm{1.4151617...}$

The real numbers that can not be represented in $\frac{p}{q}$ form are known as irrational numbers, where p and q are integers and q is not equal to zero.

$1.2$ is a terminating decimal, which can be expressed as $\frac{p}{q}$ form i.e. $\frac{12}{10},$ so it is a rational number.

$\mathrm{0.3030030003...}$ is a non-terminating and non-repeating decimal, which cannot be expressed as $\frac{p}{q}$ form, so it is an irrational number.

$\mathrm{1.4151617...}$ is a non-terminating and non-repeating decimal, which cannot be expressed as $\frac{p}{q}$ form, so it is an irrational number.

$\sqrt{4}=2$ can be expressed as $\frac{p}{q}$ form i.e. $\frac{2}{1},$ so it is a rational number.