Answer:
see explanation
Step-by-step explanation:
We require to create 2 equations with the repeating value placed after the decimal point.
let x = 2.1616...... → (1) Multiply both sides by 100
100x = 216.1616..... → (2)
Subtract (1) from (2) to eliminate the repeating decimal.
99x = 214 ( divide both sides by 99 )
x = [tex]\frac{214}{99}[/tex] = 2 [tex]\frac{16}{99}[/tex] as a mixed number
Thus
2.1616...... = [tex]\frac{214}{99}[/tex] = 2 [tex]\frac{16}{99}[/tex]
