Question

A dish containing bacteria has a diameter of 0.0001 kilometer. The diameter of a bacterium is 10−16
kilometer. How many times as large is the diameter of the dish as the diameter of the bacterium?

Answer 1

To find how many times larger the diameter of the dish is compared to the diameter of the bacterium, we can use the formula:

\[
\text{Ratio} = \frac{\text{Diameter of dish}}{\text{Diameter of bacterium}}
\]

Given:
- Diameter of the dish = \(0.0001\) kilometers
- Diameter of a bacterium = \(10^{-16}\) kilometers

Substituting the values into the formula gives:

\[
\text{Ratio} = \frac{0.0001}{10^{-16}}
\]

To divide, we can rewrite \(0.0001\) in scientific notation:

\[
0.0001 = 10^{-4}
\]

Now we substitute that into the ratio:

\[
\text{Ratio} = \frac{10^{-4}}{10^{-16}}
\]

Using the properties of exponents (specifically \( \frac{a^m}{a^n} = a^{m-n} \)), we can simplify this:

\[
\text{Ratio} = 10^{-4 - (-16)} = 10^{-4 + 16} = 10^{12}
\]

Thus, the diameter of the dish is \(10^{12}\) times larger than the diameter of the bacterium.

So, the final answer is:

\[
\text{The diameter of the dish is } 10^{12} \text{ times larger than the diameter of the bacterium.}
\]