Q10. - Algebra 1

Question

ASTRONOMY Physicists estimate that the number of stars in the universe has an order of magnitude of ${\mathbf{10}}^{21}$. The number of stars in the Milky Way galaxy is around 100 billion. Using orders of magnitude, how many times as many stars are there in the universe as the Milky Way?

Step-by-Step Solution

Answer

There are ${\mathbf{10}}^{10}$ times more stars in the universe than Milky Way galaxy.

Step 1. Write 100 billion in terms of 10 m .

100 billion means $100,000,000,000$, that is, ${10}^{11}$.

Step 2. Write the rule of quotient of powers.

For any nonzero number x, and any integers m and n, $\frac{x^m}{x^n}=x^{m-n}$.

Step 3. Apply the rule of quotient of powers and simplify.

Apply the rule of quotient of powers and simplify further.

$$\begin{gathered} \frac{{10}^{21}}{{10}^{11}}={10}^{21-11} \\ ={10}^{10} \end{gathered}$$

Therefore, there are ${10}^{10}$ times more stars in the universe than Milky Way galaxy.