1. **State the problem:** We have two circular arcs with the same center O and an angle of 120° each. The smaller arc has radius 1 cm, and the larger arc has radius 5 cm. We need to find how much longer the big arc is than the small arc, rounded to 1 decimal place. 2. **Formula for arc length:** The length $L$ of an arc with radius $r$ and central angle $\theta$ (in degrees) is given by: $$L = 2\pi r \times \frac{\theta}{360}$$ 3. **Calculate the small arc length:** $$L_{small} = 2\pi \times 1 \times \frac{120}{360} = 2\pi \times 1 \times \frac{1}{3} = \frac{2\pi}{3}$$ 4. **Calculate the big arc length:** $$L_{big} = 2\pi \times 5 \times \frac{120}{360} = 2\pi \times 5 \times \frac{1}{3} = \frac{10\pi}{3}$$ 5. **Find the difference:** $$L_{big} - L_{small} = \frac{10\pi}{3} - \frac{2\pi}{3} = \frac{(10 - 2)\pi}{3} = \frac{8\pi}{3}$$ 6. **Calculate the numerical value:** $$\frac{8\pi}{3} \approx \frac{8 \times 3.1416}{3} = \frac{25.1328}{3} \approx 8.3776$$ 7. **Round to 1 decimal place:** $$8.4$$ **Final answer:** The big arc is approximately 8.4 cm longer than the small arc.