Step 1 :Convert the mass from kilograms to milligrams using the conversion factor 1 kg = 1,000,000 mg. So, \(0.3588 \text{ kg} = 0.3588 \times 1,000,000 \text{ mg} = 358,800 \text{ mg}\).
Step 2 :Divide the total mass by the number of washers to find the mass of a single washer: \(\frac{358,800 \text{ mg}}{1000 \text{ washers}} = 358.8 \text{ mg/washer}\).
Step 3 :\(\boxed{358.8 \text{ mg/washer}}\) is the mass of a single washer.