Question

Which fraction is equal to 0.370 repeating ?

Answer 1

The answer is D. 10/27

EDG. 2021

Answer 2

Depending on which digits are being repeated, you could have

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

`1000x-x=999x=370\implies x=(370)/(999)=(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=(367)/(990)`

Or, you could have

`x=0.37\overline0=0.37=(37)/(100)`