Answer:
[tex]\frac{1}{6}[/tex]
Step-by-step explanation:
We require to create 2 equations with the repeating 6 placed after the decimal point. Then subtracting the equations eliminates the repeating part.
let x = 0.1666....... ( multiply both sides by 10 and 100 )
10x = 1.666...... → (1)
100x = 16.666...... → (2)
Subtract (1) from (2) to eliminate the repeating decimal, thus
90x = 15 ( divide both sides by 90 )
x = [tex]\frac{15}{90}[/tex] = [tex]\frac{1}{6}[/tex]
Thus
0.16666......... = [tex]\frac{1}{6}[/tex]
