Question

1.1(3) as a simplified fraction

Answer 1

`\large\boxed{1.1(3)=1(2)/(15)=(17)/(15)}`

Explanation:

`1.1(3)=1+0.1(3)=1+0.1333...\\\\\text{Let}\ x=0.1333...\qquad\text{multiply both sides by 10}\\\\10x=1.333...\qquad\texT{multiply both sides by 10}\\\\100x=13.333...\qquad\text{make different}\\\\100x-10x=13.333...-1.333...\\\\90x=12\qquad\text{divide both sides by 90}\\\\x=(12)/(90)\\\\x=(12:6)/(90:6)\\\\x=(2)/(15)`