The radius of the earth is 6.37*10^6 m and its mass is 5.975*10^24 kg. Find the earth's average density to appropriate significant figure.

To find the Earth's average density, we need to use the formula:

Density = Mass / Volume

To find the volume of the Earth, we can use the formula for the volume of a sphere:

Volume = (4/3)πr³

First, let's calculate the volume using the given radius:

Volume = (4/3)π(6.37*10^6)³

Now, let's calculate the mass to volume ratio by dividing the mass by the volume:

Density = (5.975*10^24) / [(4/3)π(6.37*10^6)³]

To get the answer in appropriate significant figures, we need to round the final result to the appropriate number of digits. Since we are given the radius and mass with three significant figures, we will round the density to three significant figures as well.

Finally, we can plug in the values and calculate the answer to find the Earth's average density.