Subjects unit conversion

Mass Conversion F21A7D

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1. **State the problem:** We are given the mass of one item as 45 t (tonnes), 81 kg, 31 dag, and 9 mg. We need to find the total mass when multiplied by the given factor (implied multiplication by 1 here, so just convert the units properly). 2. **Understand the units:** - 1 t = 1000 kg - 1 kg = 10 dag - 1 dag = 10 g (grams), but since grams are not listed, we continue with dg and mg - 1 dag = 100 dg - 1 dg = 10 mg 3. **Convert all units to a single unit for easier calculation, for example, kilograms:** - Convert tonnes to kilograms: $$45 \text{ t} = 45 \times 1000 = 45000 \text{ kg}$$ - Kilograms remain as is: $$81 \text{ kg}$$ - Convert decagrams to kilograms: $$31 \text{ dag} = 31 \times 0.01 = 0.31 \text{ kg}$$ - Convert milligrams to kilograms: $$9 \text{ mg} = 9 \times 10^{-6} = 0.000009 \text{ kg}$$ 4. **Add all converted values:** $$45000 + 81 + 0.31 + 0.000009 = 45081.310009 \text{ kg}$$ 5. **Express the total mass in tonnes and kilograms:** - Convert kilograms back to tonnes and kilograms: $$45081.310009 \text{ kg} = 45 \text{ t} + 81.310009 \text{ kg}$$ - Separate kilograms and grams (if needed): $$0.310009 \text{ kg} = 310.009 \text{ g}$$ 6. **Final answer:** The total mass is approximately **45 t 81 kg 310 g**.