Answer:
The fraction is [tex]\frac{7}{6}[/tex]
Step-by-step explanation:
we have
[tex]1.166666666...[/tex]
This is a repeating decimal
Convert to fraction number
Let
[tex]x=1.1666666...[/tex]
[tex]10x=11.6666666...[/tex]
[tex]100x=116.666666...[/tex]
[tex]100x-10x=116.666...-11.666...[/tex]
[tex]90x=105[/tex]
Solve for x
Divide by 90 both sides
[tex]x=\frac{105}{90}[/tex]
Simplify
Divide both numerator and denominator by 15
[tex]x=\frac{7}{6}[/tex]
