1. **State the problem:** We need to divide 434 by 0.87. 2. **Write the division expression:** $$434 \div 0.87$$ 3. **Convert the divisor to a whole number:** Multiply numerator and denominator by 100 to eliminate the decimal in the divisor. $$\frac{434}{0.87} = \frac{434 \times 100}{0.87 \times 100} = \frac{43400}{87}$$ 4. **Perform the division:** Divide 43400 by 87. 5. **Calculate:** $$87 \times 498 = 43326$$ $$43400 - 43326 = 74$$ So, the quotient is approximately 498 with a remainder 74. 6. **Express as decimal:** $$\frac{74}{87} \approx 0.8506$$ 7. **Final answer:** $$434 \div 0.87 \approx 498.85$$