Question

Show that the following number is rational: 7.526262626... show all work, discrete math

Answer 1

$x=7.5\overline{26}\\10x=75.\overline{26}\\1000x=7526.\overline{26}\\1000x-10x=7526.\overline{26}-75.\overline{26}\\990x=7451\\x=\dfrac{7451}{990}$

It can be expressed as a fraction with integer numerator and denominator, so it's a rational number.