Question

Mass of earth is ($5.97\times {10}^{24}$) kg and mass of moon is ($7.35\times {10}^{22}$) kg. What is the total mass of the two?

Answer 1

Mass of the Earth $=5.97\times {10}^{24}kg$

Now, $5.97\times {10}^{24}=5.97\times {10}^{(2+22)}=5.97\times {10}^2\times {10}^{22}=597\times {10}^{22}$

So, the mass of the Earth can also be written as $597\times {10}^{22}kg.$
Mass of the Moon $=7.35\times {10}^{22}kg$

Sum of the masses of the Earth and the Moon:

$=597\times {10}^{22}+7.35\times {10}^{22}$

$=(597+7.35)\times {10}^{22}$

$=604.35\times {10}^{22}$

$=6.0435\times 100\times {10}^{22}$

$=6.0435\times {10}^2\times {10}^{22}$

$=6.0435\times {10}^{(2+22)}$

$=6.0435\times {10}^{24}kg$