Question

solve the problem. use the correct number of significant digits. 9) assume that the volume of the earth is 4.9 x 10^14 cubic meters and the volume of a bacterium is 4.6 x 10^-16 cubic meters. if the earth could be filled with bacteria, how many would it contain?

Explanation:

Step1: Set up the division formula

To find the number of bacteria that can fill the Earth, we divide the volume of the Earth by the volume of a single bacterium. Let $N$ be the number of bacteria. The formula is $N=\frac{V_{Earth}}{V_{bacterium}}$, where $V_{Earth} = 4.9\times10^{14}$ cubic - meters and $V_{bacterium}=4.6\times 10^{-16}$ cubic - meters.

Step2: Perform the division

Using the rule of dividing numbers in scientific notation $\frac{a\times10^{m}}{b\times10^{n}}=\frac{a}{b}\times10^{m - n}$, we have $N=\frac{4.9}{4.6}\times10^{14-(-16)}$.
First, calculate $\frac{4.9}{4.6}\approx1.0652$. Then, $14-(-16)=14 + 16=30$. So $N\approx1.0652\times10^{30}$.

Step3: Determine the number of significant digits

The number 4.9 has 2 significant digits and 4.6 has 2 significant digits. So our result should have 2 significant digits. Rounding 1.0652 to 2 significant digits gives 1.1. So $N = 1.1\times10^{30}$.

Answer:

$1.1\times10^{30}$