Scientific Notation Operations Math Example 4

Follow the full solution, then compare it with the other examples linked below.

Example 4

medium

The mass of the Earth is

5.97 \times 10^{24}

kg. The mass of the Moon is

7.35 \times 10^{22}

kg. How many times heavier is the Earth than the Moon?

Solution

1
Divide: $\dfrac{5.97 \times 10^{24}}{7.35 \times 10^{22}} = \dfrac{5.97}{7.35} \times 10^{24-22}$ .
2
$\dfrac{5.97}{7.35} \approx 0.8122$ . And $10^{24-22} = 10^2$ .
3
Adjust: $0.8122 \times 10^2 = 8.122 \times 10^1 \approx 81.2$ .

Answer

The Earth is approximately

81

times heavier than the Moon.

Dividing two scientific notation numbers follows the same structure as multiplying: handle coefficients and exponents separately. When the coefficient quotient is less than