Question

State whether the given statement is true/false:

An irrational number between two numbers $\frac{1}{7}$ and $\frac{2}{7}$ is $0.1501500\mathrm{15000...}$

• A. True
• B. False

Answer 1

The correct option is A True

The decimal forms of the given numbers as follows:

$\frac{1}{7}=0.\overline{142857}$ and $\frac{2}{7}=0.\overline{285714}$.

Since, they are non-terminating recurring, the given numbers are rational.

We know, an irrational number is a number which is non-terminating non-recurring.

Between two rational numbers, we can find infinitely many irrational numbers.

The given number, $\mathrm{0.150150015000...}$ is irrational as it is non-terminating non-repeating.

Also, $0.\overline{142857}<\mathrm{0.150150015000...}<0.\overline{285714}$.

That is, $\mathrm{0.150150015000...}$ lies between $\frac{1}{7}$ and $\frac{2}{7}$.

Hence, $\mathrm{0.150150015000...}$ is an irrational number between two numbers $\frac{1}{7}$ and and $\frac{2}{7}$ and the statement is true.