Question

Express the following repeating decimal as a fraction in simplest form.

Answer 1

Answer:

$0.\overline{369} = \frac{41}{111}$

Step-by-step explanation:

x = 0.369369369...

10x = 3.69369369...

100x = 36.9369369...

1000x = 369.369369...

1000x - x = 369

999x = 369

$x = \frac{369}{999} \\\\x = \frac{123}{333}\\\\x = \frac{41}{111}$