To determine how many times smaller a bacterial cell is than an amoeba cell, follow these detailed steps:
1. Identify the lengths:
- The length of a bacterial cell is: [tex]\(3 \times 10^{-6} \, \text{meters}\)[/tex]
- The length of an amoeba cell is: [tex]\(4.5 \times 10^{-4} \, \text{meters}\)[/tex]
2. Calculate the ratio of the lengths:
[tex]\[
\text{Ratio} = \frac{\text{Length of amoeba}}{\text{Length of bacterium}}
\][/tex]
Plugging in the values:
[tex]\[
\text{Ratio} = \frac{4.5 \times 10^{-4}}{3 \times 10^{-6}}
\][/tex]
3. Simplify the ratio:
- First, divide the numerical part:
[tex]\[
\frac{4.5}{3} = 1.5
\][/tex]
- Next, divide the powers of 10:
[tex]\[
\frac{10^{-4}}{10^{-6}} = 10^{-4 - (-6)} = 10^{-4 + 6} = 10^2
\][/tex]
- Combine the two parts:
[tex]\[
1.5 \times 10^{2}
\][/tex]
4. Express the answer in scientific notation:
The result [tex]\(1.5 \times 10^{2}\)[/tex] is already in scientific notation, and it has the correct significant digits based on the provided lengths.
So, the bacterial cell is [tex]\(1.5 \times 10^{2}\)[/tex] times smaller than the amoeba cell.
5. Compare with provided choices:
The closest choice to [tex]\(1.5 \times 10^2\)[/tex] in the given options is:
[tex]\[
\boxed{2 \times 10^2}
\][/tex]
