Answer:
[tex]\large\boxed{1.1(3)=1\dfrac{2}{15}=\dfrac{17}{15}}[/tex]
Step-by-step explanation:
[tex]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=\dfrac{12}{90}\\\\x=\dfrac{12:6}{90:6}\\\\x=\dfrac{2}{15}[/tex]
