Subjects unit conversion

Volume Conversion Abb905

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1. **State the problem:** We need to convert 1.24 ML (megaliters) of water into dm³ (cubic decimeters) and µm³ (cubic micrometers). 2. **Recall unit conversions:** - 1 ML = $10^6$ L - 1 L = 1 dm³ - 1 m = $10^6$ µm 3. **Convert ML to dm³:** Since 1 L = 1 dm³, then $$\text{Volume in dm}^3 = 1.24 \times 10^6 \text{ dm}^3$$ 4. **Convert ML to µm³:** First, convert 1.24 ML to m³: $$1.24 \text{ ML} = 1.24 \times 10^6 \text{ L} = 1.24 \times 10^3 \text{ m}^3$$ Since 1 m = $10^6$ µm, then $$1 \text{ m}^3 = (10^6 \text{ µm})^3 = 10^{18} \text{ µm}^3$$ Therefore, $$\text{Volume in µm}^3 = 1.24 \times 10^3 \times 10^{18} = 1.24 \times 10^{21} \text{ µm}^3$$ 5. **Final answers:** - Volume in dm³: $1.24 \times 10^6$ dm³ - Volume in µm³: $1.24 \times 10^{21}$ µm³ This shows how to convert large volumes into different cubic units by using powers of ten and unit equivalences.