Question

The moon has a mass of 7.35×10^22 KG while earth has a mass of 5.97×10^24 KG what is the combined mass of the earth and moon

Answer 1

The combined mass of earth and moon is $6.0435 \times 10^{24}$ kg

Solution:

Given that moon has a mass of $7.35 \times 10^{22}$ kg while the earth has mass of $5.97 \times 10^{24}$ kg

To find: combined mass of earth and moon

From given question,

mass of earth = $5.97 \times 10^{24}$ kg

mass of moon = $7.35 \times 10^{22}$ kg

Combined mass = mass of earth + mass of moon

Substituting the values we get,

$\text{ Combined mass } = 5.97 \times 10^{24} + 7.35 \times 10^{22}$

Make both the exponents same

Move the decimal point two times left in $7.35 \times 10^{22}$ and increase the exponent to $10^{24}$

$\text{ Combined mass } = 5.97 \times 10^{24} + 0.0735 \times 10^{24}$

Take $10^{24}$ as common term

$\text{ Combined mass } = 10^{24} (5.97 + 0.0735)\\\\\text{ Combined mass } = 6.0435 \times 10^{24}$

Thus combined mass of earth and moon is $6.0435 \times 10^{24}$ kg