Question

Say true or false.

An irrational number between $7.403\overline{12}$ and $7.4\overline{04}$ is $7.403\overline{45}$.

• A. True
• B. False

Answer 1

The correct option is B False

Lets consider the term $\mathrm{7.40345345345345.....}$
Let $x=\mathrm{7.40345345....}$
$100x=\mathrm{740.345345....}$
$100000x=\mathrm{740345.345....}$
Subtracting two equations we get $99900x=739605$
$x=739605/99900$
Thus, its a rational number and thus the statement is false.