To determine how many times smaller the bacterial cell is compared to the amoeba cell, you can divide the length of the amoeba cell by the length of the bacterial cell.
The lengths are:
- Bacterial cell: \( 4 \times 10^{-6} \) m
- Amoeba cell: \( 2.5 \times 10^{-4} \) m
Now, let's perform the calculation:
\[ \frac{\text{Length of amoeba cell}}{\text{Length of bacterial cell}} = \frac{2.5 \times 10^{-4}}{4 \times 10^{-6}} \]
To simplify this division, you can divide the coefficients (2.5 divided by 4) and subtract the exponents (−4 minus −6).
Calculating the coefficients:
\[ \frac{2.5}{4} = 0.625 \]
Now for the exponents:
\[ -4 - (-6) = -4 + 6 = 2 \]
Putting it all together:
\[ 0.625 \times 10^{2} \]
To express \(0.625\) in scientific notation, this can be rewritten:
\[ 0.625 \times 10^2 = 6.25 \times 10^{1} \]
Thus, the amoeba cell is \(6.25 \times 10^{1}\) times larger than the bacterial cell. Therefore, the bacterial cell is
\[ \frac{1}{6.25 \times 10^{1}} = 6.25 \times 10^{2} \text{ times smaller than the amoeba cell.} \]
So, the correct answer is:
6.25 x 102.
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