Question

Which fraction is equal to 0.370 repeating ?

Answer 1

Depending on which digits are being repeated, you could have

$x=0.\overline{370}\implies1000x=370.\overline{370}$

$1000x-x=999x=370\implies x=\dfrac{370}{999}=\dfrac{10}{27}$

Or, you could have

$x=0.3\overline{70}\implies10x=3.\overline{70}\implies1000x=370.\overline{70}$

$1000x-10x=990x=367\implies x=\dfrac{367}{990}$

Or, you could have

$x=0.37\overline0=0.37=\dfrac{37}{100}$