1. **State the problem:** Calculate the value of the expression $2 \times 115 \div 360 \times \frac{22}{7} \times 25 \times 25$. 2. **Write the expression clearly:** $$2 \times 115 \div 360 \times \frac{22}{7} \times 25 \times 25$$ 3. **Simplify step-by-step:** - Multiply the constants and fractions carefully. 4. **Calculate numerator and denominator separately:** - Numerator: $2 \times 115 \times 22 \times 25 \times 25$ - Denominator: $360 \times 7$ 5. **Calculate numerator:** $$2 \times 115 = 230$$ $$230 \times 22 = 5060$$ $$5060 \times 25 = 126500$$ $$126500 \times 25 = 3162500$$ 6. **Calculate denominator:** $$360 \times 7 = 2520$$ 7. **Divide numerator by denominator:** $$\frac{3162500}{2520}$$ 8. **Perform the division:** $$3162500 \div 2520 = 1255.5555...$$ 9. **Final answer:** $$\boxed{1255.56}$$ (rounded to two decimal places)