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The earth has a mass of approximately 6*10^(24) kilograms (kg). The volume of the earth's oceans is approximately 1.34*10^(9) cubic kilometers (km^(3)), and ocean water has a mass of about 1.03*10^(12)(kg)/(km^(3)). To the nearest hundredth of a percent, what percent of the earth's mass is from the oceans? (Ignore the % symbol when entering your answer. For example, if the answer is 0.11%, enter 0.11 .)

The earth has a mass of approximately 6⋅1024 6 \cdot 10^{24} kilograms (kg) (\mathrm{kg}) . The volume of the earth's oceans is approximately 1.34⋅109 1.34 \cdot 10^{9} cubic kilometers (km3) \left(\mathrm{km}^{3}\right) , and ocean water has a mass of about 1.03⋅1012kgkm3 1.03 \cdot 10^{12} \frac{\mathrm{kg}}{\mathrm{km}^{3}} . To the nearest hundredth of a percent, what percent of the earth's mass is from the oceans?\newline(Ignore the % \% symbol when entering your answer. For example, if the answer is 0.11% 0.11 \% , enter 00.1111 .)

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Q. The earth has a mass of approximately 6⋅1024 6 \cdot 10^{24} kilograms (kg) (\mathrm{kg}) . The volume of the earth's oceans is approximately 1.34⋅109 1.34 \cdot 10^{9} cubic kilometers (km3) \left(\mathrm{km}^{3}\right) , and ocean water has a mass of about 1.03⋅1012kgkm3 1.03 \cdot 10^{12} \frac{\mathrm{kg}}{\mathrm{km}^{3}} . To the nearest hundredth of a percent, what percent of the earth's mass is from the oceans?\newline(Ignore the % \% symbol when entering your answer. For example, if the answer is 0.11% 0.11 \% , enter 00.1111 .)
  1. Identify given values: Identify the given values for the mass of the Earth and the volume and mass density of the oceans.\newlineMass of the Earth Mearth=6×1024M_{\text{earth}} = 6 \times 10^{24} kg\newlineVolume of the Earth's oceans Voceans=1.34×109V_{\text{oceans}} = 1.34 \times 10^{9} km3^3\newlineMass density of ocean water ρocean=1.03×1012\rho_{\text{ocean}} = 1.03 \times 10^{12} kg/km3^3
  2. Calculate mass of the Earth's oceans: Calculate the total mass of the Earth's oceans by multiplying the volume of the oceans by the mass density of ocean water.\newlineMass of oceans Moceans=Voceans×ρoceanM_{\text{oceans}} = V_{\text{oceans}} \times \rho_{\text{ocean}}\newlineMoceans=(1.34×109 km3)×(1.03×1012 kg/km3)M_{\text{oceans}} = (1.34 \times 10^9 \text{ km}^3) \times (1.03 \times 10^{12} \text{ kg/km}^3)\newlineMoceans=1.34×1.03×109+12 kgM_{\text{oceans}} = 1.34 \times 1.03 \times 10^{9+12} \text{ kg}\newlineMoceans=1.3802×1021 kgM_{\text{oceans}} = 1.3802 \times 10^{21} \text{ kg}
  3. Calculate percentage of Earth's mass from oceans: Calculate the percentage of the Earth's mass that is from the oceans by dividing the mass of the oceans by the mass of the Earth and then multiplying by 100100 to convert it to a percentage.\newlinePercentage of Earth's mass from oceans = (Moceans/Mearth)×100(M_{\text{oceans}} / M_{\text{earth}}) \times 100\newlinePercentage of Earth's mass from oceans = (1.3802×1021 kg)/(6×1024 kg)×100(1.3802 \times 10^{21} \text{ kg}) / (6 \times 10^{24} \text{ kg}) \times 100\newlinePercentage of Earth's mass from oceans = (1.3802/6)×10−3×100(1.3802 / 6) \times 10^{-3} \times 100\newlinePercentage of Earth's mass from oceans = 0.23003×10−1×1000.23003 \times 10^{-1} \times 100\newlinePercentage of Earth's mass from oceans = 00.2300323003\%
  4. Round the percentage: Round the percentage to the nearest hundredth of a percent. Rounded percentage = 0.23%0.23\%

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