The volume of Earth is on the order of 10^21 m^3. (a) What is this in cubic kilometers (km^3) ?

step 1 Hello and welcome to this video solution of numerate. So here it's given that the volume of eart

The volume of Earth is on the order of 10^21 m^3. (a) What...

The volume of Earth is on the order of $10^{21} \mathrm{m}^{3}$. (a) What is this in cubic kilometers $\left(\mathrm{km}^{3}\right) ?$ (b) What is it in cubic miles (mi $^{3}$ )? (c) What is it in cubic centimeters $\left(\mathrm{cm}^{3}\right) ?$

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Key Concepts

Orders of Magnitude and Scientific Notation

Using orders of magnitude and scientific notation allows for easy manipulation and understanding of very large or very small numbers. In the problem, large volumes are expressed as powers of 10, making it simpler to carry out conversions and maintain clarity in calculations when transitioning between units such as cubic meters, cubic kilometers, cubic miles, and cubic centimeters.

Unit Conversion

Unit conversion is the process of converting a measurement expressed in one set of units to another, using conversion factors. This concept is essential in fields such as physics and engineering to ensure that quantities are expressed in consistent and practical units.

Volume Conversion

Volume conversion involves changing a measurement from one cubic unit to another. Because volume scales with the cube of the linear dimension, the conversion factor between units must be cubed. For example, converting from meters to kilometers requires cubing the linear conversion (1 km = 1000 m) to obtain that 1 m³ = 10?? km³.

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