1. **State the problem:** We need to evaluate the division of two decimal numbers: $0.004560 \div 2.13$. 2. **Formula used:** Division of decimals can be done by converting the divisor to a whole number and adjusting the dividend accordingly. 3. **Step-by-step solution:** - Multiply both numerator and denominator by 100 to eliminate decimals in the divisor: $$\frac{0.004560 \times 100}{2.13 \times 100} = \frac{0.456}{213}$$ - Now divide $0.456$ by $213$: $$0.456 \div 213 = \frac{0.456}{213}$$ - Perform the division: $$0.456 \div 213 \approx 0.00214$$ 4. **Explanation:** Multiplying numerator and denominator by the same number does not change the value of the fraction. This makes division easier by removing decimals from the divisor. 5. **Final answer:** $$0.004560 \div 2.13 \approx 0.00214$$