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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 $6 \cdot 10^{24}$ kilograms $(\mathrm{kg})$ . The volume of the earth's oceans is approximately $1.34 \cdot 10^{9}$ cubic kilometers $\left(\mathrm{km}^{3}\right)$ , and ocean water has a mass of about $1.03 \cdot 10^{12} \frac{\mathrm{kg}}{\mathrm{km}^{3}}$ . 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 $0.11 \%$ , enter $0$ . $11$ .)

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Find what percent one number is of another: word problems

Full solution

Q. The earth has a mass of approximately

6 \cdot 10^{24}

kilograms

(\mathrm{kg})

. The volume of the earth's oceans is approximately

1.34 \cdot 10^{9}

cubic kilometers

\left(\mathrm{km}^{3}\right)

, and ocean water has a mass of about

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 \%

, enter

0

.

11

.)

Identify given values: Identify the given values for the mass of the Earth and the volume and mass density of the oceans. $\newline$ Mass of the Earth $M_{\text{earth}} = 6 \times 10^{24}$ kg $\newline$ Volume of the Earth's oceans $V_{\text{oceans}} = 1.34 \times 10^{9}$ km $^3$ $\newline$ Mass density of ocean water $\rho_{\text{ocean}} = 1.03 \times 10^{12}$ kg/km $^3$
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. $\newline$ Mass of oceans $M_{\text{oceans}} = V_{\text{oceans}} \times \rho_{\text{ocean}}$ $\newline$ $M_{\text{oceans}} = (1.34 \times 10^9 \text{ km}^3) \times (1.03 \times 10^{12} \text{ kg/km}^3)$ $\newline$ $M_{\text{oceans}} = 1.34 \times 1.03 \times 10^{9+12} \text{ kg}$ $\newline$ $M_{\text{oceans}} = 1.3802 \times 10^{21} \text{ kg}$
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 $100$ to convert it to a percentage. $\newline$ Percentage of Earth's mass from oceans = $(M_{\text{oceans}} / M_{\text{earth}}) \times 100$ $\newline$ Percentage of Earth's mass from oceans = $(1.3802 \times 10^{21} \text{ kg}) / (6 \times 10^{24} \text{ kg}) \times 100$ $\newline$ Percentage of Earth's mass from oceans = $(1.3802 / 6) \times 10^{-3} \times 100$ $\newline$ Percentage of Earth's mass from oceans = $0.23003 \times 10^{-1} \times 100$ $\newline$ Percentage of Earth's mass from oceans = $0$ . $23003$ \%
Round the percentage: Round the percentage to the nearest hundredth of a percent. Rounded percentage = $0.23\%$

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