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A Li-ion battery system presents a lifetime of 12 000 cycles of complete charge and discharge. When a cycle is not completely discharging the battery, the cycle is weighted by the depth of discharge for such cycle. For instance, if the battery is discharge by 10 % for a cycle, we can count this cycle as 0.1 to evaluate the battery lifetime. The analysis of the production and the consumption indicates that 1 full cycle per day is required and 3 small cycles with 31.4% depth of discharge per day are needed to ensure the energy balance. We wish to evaluate the impact of the small cycle in the lifetime of the battery system. Hence we should compute the battery lifetime with and without considering the small cycles. Evaluate the ratio, with 3 decimals, between the battery lifetime with the small cycle and he battery lifetime without the small cycles. Answer: