Answer:
[tex]\frac{1}{6}[/tex]
Step-by-step explanation:
We require to create 2 equations with the repeating digit (6) after the decimal point.
let x = 0.166.... ( multiply both sides by 10 and 100 )
10x = 1.66.... → (1)
100x = 16.66..... → (2)
Subtract (1) from (2) eliminating the repeating decimal
90x = 15 ( divide both sides by 90 )
x = [tex]\frac{15}{90}[/tex] = [tex]\frac{1}{6}[/tex]
Thus
0.166...... = [tex]\frac{1}{6}[/tex]
