1. **Problem:** Evaluate the expression $$\frac{0.13 \times 0.3 - 0.003}{0.09}$$ without using a calculator or tables. 2. **Formula and rules:** Multiplication and subtraction of decimals, then division. 3. **Step 1:** Multiply $0.13$ by $0.3$: $$0.13 \times 0.3 = 0.039$$ 4. **Step 2:** Subtract $0.003$ from $0.039$: $$0.039 - 0.003 = 0.036$$ 5. **Step 3:** Divide the result by $0.09$: $$\frac{0.036}{0.09}$$ 6. **Step 4:** Simplify the division by expressing both numerator and denominator as fractions: $$0.036 = \frac{36}{1000}, \quad 0.09 = \frac{9}{100}$$ 7. **Step 5:** Rewrite the division: $$\frac{36/1000}{9/100} = \frac{36}{1000} \times \frac{100}{9} = \frac{36 \times 100}{1000 \times 9} = \frac{3600}{9000}$$ 8. **Step 6:** Simplify the fraction: $$\frac{3600}{9000} = \frac{36}{90} = \frac{2}{5} = 0.4$$ **Final answer:** $0.4$