1. The problem is to calculate $2 - \frac{2}{9}$.\n\n2. To subtract a fraction from a whole number, convert the whole number to a fraction with the same denominator. Here, $2 = \frac{18}{9}$.\n\n3. Now subtract the fractions: $$\frac{18}{9} - \frac{2}{9} = \frac{18 - 2}{9} = \frac{16}{9}.$$\n\n4. The fraction $\frac{16}{9}$ is an improper fraction and can be expressed as a mixed number: $$1 \frac{7}{9}.$$\n\n5. Therefore, the final answer is $\frac{16}{9}$ or $1 \frac{7}{9}$.