Given that the world's oceans comtain 1.35 x 10(to the 9th power)km³ of water, determine the mass in grams. Show how to obtain conversion factors from km³ to m³, report value in proper scientific notation using the correct number of significant figures.
and m³ to cm³
1 km = 1000 m; therefore, 1 km^3 = 1,000^3 m^3
Do the other factors the same way. Look up the density of sea water.
mass = volume x density. Post your work if you get stuck.
To determine the mass of the world's oceans in grams, we need to convert the volume of water from km³ to m³ and then multiply it by the density of water.
1. Start with the given volume of water in km³: 1.35 x 10⁹ km³.
2. Convert km³ to m³ by using the conversion factor 1 km = 1000 meters in each dimension (length, width, and height). Since volume is measured in cubic units, we need to cube the conversion factor:
(1 km)³ = (1000 m)³ = 1,000,000,000 m³
Therefore, 1 km³ = 1,000,000,000 m³.
3. Multiply the volume in m³ by the density of water. The density of water is approximately 1 gram per cubic centimeter (g/cm³) or 1000 kilograms per cubic meter (kg/m³). Since we need the answer in grams, we will use 1000 kg/m³.
(1,350,000,000,000 m³) * (1000 kg/m³) = 1,350,000,000,000,000 kg.
4. Finally, convert kilograms to grams using the conversion factor 1 kilogram (kg) = 1000 grams (g):
1,350,000,000,000,000 kg * 1000 g/kg = 1.35 x 10¹⁸ g.
Therefore, the mass of the world's oceans is approximately 1.35 x 10¹⁸ grams.