Let's substitute the values of $a = 2$ and $b = 9$ into the expression $2a^2 - \frac{1}{3b}$.

Given: $2a^2 - \frac{1}{3b}$

Substituting the values: $2(2)^2 - \frac{1}{3(9)}$

Simplify:

1. Calculate $2^2$: $2^2 = 4$
2. Multiply by 2: $2 \times 4 = 8$
3. Calculate $3 \times 9$: $3 \times 9 = 27$
4. Calculate $\frac{1}{27}$: $\frac{1}{27} \approx 0.037$

Final expression: $8 - 0.037 \approx 7.963$

So, the value of the expression is approximately $7.963$.

Would you like further details or have any questions? Here are some related questions:

1. How do you simplify expressions with fractions?
2. What happens when you change the values of $a$ and $b$?
3. Can you solve similar expressions involving roots or powers?
4. How can we round decimals to different places?
5. How do expressions with variables behave in equations?

Tip: Always simplify inside the parentheses first when substituting values into an expression.