Subjects unit conversions

Volume Conversions

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Volume Conversions


1. **Stating the problem:** We need to complete volume unit conversions between cubic meters (m³), cubic decimeters (dm³), cubic centimeters (cm³), cubic millimeters (mm³), and liters (l).\n\n2. **Important formulas and rules:**\n- $1\,m^3 = 1000\,dm^3$\n- $1\,dm^3 = 1000\,cm^3$\n- $1\,cm^3 = 1000\,mm^3$\n- $1\,dm^3 = 1\,l$ (liter)\n- $1\,dal = 10\,l$\n- $1\,hl = 100\,l$\n- $1\,cl = 0.01\,l$\n- $1\,ml = 0.001\,l$\n\n3. **Conversions:**\n- $1\,m^3 = 1000\,dm^3 = 1,000,000\,cm^3$\n- $1\,dm^3 = 1000\,cm^3 = 1\,l$\n- $1\,cm^3 = 1000\,mm^3 = 0.001\,l$\n\n4. **Given values and conversions:**\n- $4.8\,m^3 = 4.8 \times 1000 = 4800\,dm^3$\n- $9,600\,l = 9600\,dm^3$ (since $1\,l = 1\,dm^3$)\n- $842\,mm^3 = \frac{842}{1000} = 0.842\,cm^3$\n- $0.842\,cm^3 = 0.000842\,l$ (since $1\,cm^3 = 0.001\,l$)\n- $24.79\,cm^3 = \frac{24.79}{1000} = 0.02479\,dm^3$\n- $0.02479\,dm^3 = 0.02479\,l$\n\n5. **Recanier et complète:**\n- $50\,ml = 50\,cm^3$ (since $1\,ml = 1\,cm^3$)\n- $0.48\,dm^3 = 0.48\,l$\n- $20\,cl = 20 \times 10 = 200\,ml = 200\,cm^3$\n- $1\,dm^3 = 1\,l$\n- $500\,m^3 = 500 \times 1000 = 500,000\,dl$ (since $1\,m^3 = 1000\,dm^3 = 10,000\,dl$; $1\,dl = 0.1\,dm^3$ so $500\,m^3 = 5,000,000\,dl$)\n- $1\,m^3 = 1000\,l$\n\n6. **Grouped conversions:**\n- $1000\,dm^3 = 1,000,000\,cm^3$\n- $483\,cm^3 = 0.483\,dm^3$\n- $764\,dm^3 = 0.764\,m^3$\n- $9.5\,l = 9.5\,dm^3$\n- $0.36\,hl = 36\,l$\n- $0.75\,dal = 7.5\,l$\n- $0.48\,dm^3 = 0.48\,l$\n- $1\,dm^3 = 1\,l$\n- $1\,m^3 = 1000\,l$\n\n**Final answers:**\n- $1\,m^3 = 1000\,dm^3 = 1,000,000\,cm^3$\n- $1\,dm^3 = 1000\,cm^3 = 1\,l$\n- $1\,cm^3 = 1000\,mm^3 = 0.001\,l$\n- $4.8\,m^3 = 4800\,dm^3$\n- $842\,mm^3 = 0.842\,cm^3 = 0.000842\,l$\n- $24.79\,cm^3 = 0.02479\,dm^3 = 0.02479\,l$\n- $50\,ml = 50\,cm^3 = 0.05\,dm^3 = 0.05\,l$\n- $20\,cl = 200\,ml = 200\,cm^3 = 0.2\,dm^3 = 0.2\,l$\n- $500\,m^3 = 5,000,000\,dl = 500,000\,l$