1. **Problem statement:** Convert the volume 456000 cm^3 to dam^3. 2. **Formula and rules:** To convert cubic centimeters (cm^3) to cubic decameters (dam^3), use the fact that 1 dam = 10 m = 1000 cm. Therefore, 1 dam^3 = (1000 cm)^3 = 10^9 cm^3. 3. **Conversion:** $$456000\text{ cm}^3 = \frac{456000}{10^9} \text{ dam}^3$$ 4. **Simplify:** $$= 456000 \times 10^{-9} \text{ dam}^3 = 4.56 \times 10^{-4} \text{ dam}^3$$ 5. **Explanation:** Since 1 dam^3 is a billion cm^3, dividing 456000 by 1,000,000,000 gives the volume in dam^3. The result is a very small number because cm^3 is much smaller than dam^3. **Final answer:** $$456000\text{ cm}^3 = 4.56 \times 10^{-4} \text{ dam}^3$$