1. **State the problem:** We need to evaluate the square of the number 0.0033, which means calculating $$(0.0033)^2$$. 2. **Formula used:** The square of a number $x$ is given by $$x^2 = x \times x$$. 3. **Apply the formula:** Here, $$x = 0.0033$$, so $$ (0.0033)^2 = 0.0033 \times 0.0033 $$. 4. **Perform the multiplication:** $$ 0.0033 \times 0.0033 = 0.00001089 $$. 5. **Explanation:** Multiplying two small decimals results in an even smaller decimal. We can also think of it as: $$ 0.0033 = \frac{33}{10000} $$, so $$ \left(\frac{33}{10000}\right)^2 = \frac{33^2}{10000^2} = \frac{1089}{100000000} = 0.00001089 $$. 6. **Final answer:** $$ (0.0033)^2 = 0.00001089 $$.