Question

The average human body cell is about
\[5.1 \cdot 10^{-4} \text{ cm}\] in diameter. The diameter of a plant cell is
\[8 \cdot 10^{-3} \text{ cm}\].
What is the combined diameter of the body cell and plant cell?
Express your answer in scientific notation.

Answer 1

To find the combined diameter of the body cell and the plant cell, we need to add their diameters together.

The diameter of the average human body cell is given as:
\[
5.1 \cdot 10^{-4} \text{ cm}
\]
The diameter of a plant cell is:
\[
8 \cdot 10^{-3} \text{ cm}
\]

First, we need to express both numbers in a similar form to add them. The diameter of the plant cell can be rewritten in terms of \(10^{-4}\):
\[
8 \cdot 10^{-3} \text{ cm} = 8 \cdot 10^{-3} \cdot \frac{10}{10} = 8 \cdot 10^{-3} \cdot \frac{1}{10^{-1}} = 80 \cdot 10^{-4} \text{ cm}
\]

Now we have:
- Body cell: \(5.1 \cdot 10^{-4} \text{ cm}\)
- Plant cell: \(80 \cdot 10^{-4} \text{ cm}\)

Now we can add these two terms:
\[
5.1 \cdot 10^{-4} + 80 \cdot 10^{-4} = (5.1 + 80) \cdot 10^{-4} = 85.1 \cdot 10^{-4}
\]

Next, we need to express \(85.1 \cdot 10^{-4}\) in proper scientific notation. Scientific notation requires a single non-zero digit to the left of the decimal, so we write:
\[
85.1 \cdot 10^{-4} = 8.51 \cdot 10^{1} \cdot 10^{-4} = 8.51 \cdot 10^{-3}
\]

Thus, the combined diameter of the body cell and plant cell in scientific notation is:
\[
\boxed{8.51 \cdot 10^{-3}} \text{ cm}
\]