Question

2.5×10
6
bacteria are measured to be in a dirt sample that weighs 11 gram. Use scientific notation to express the number of bacteria that would be in a sample weighing 2525 grams.
Answer
Attempt 1 out of 2

Answer:
times, 10×10
bacteria

Answer 1

To find the number of bacteria in a sample weighing 2525 grams, we can set up a proportion based on the initial data provided:

1. You have \( 2.5 \times 10^6 \) bacteria in a 11-gram sample.
2. To find the number of bacteria per gram:
\[
\text{Bacteria per gram} = \frac{2.5 \times 10^6 \text{ bacteria}}{11 \text{ grams}} \approx 2.273 \times 10^5 \text{ bacteria/gram} \quad (\text{using scientific notation})
\]

3. Now, to find the total number of bacteria in 2525 grams:
\[
\text{Total bacteria} = 2.273 \times 10^5 \text{ bacteria/gram} \times 2525 \text{ grams}
\]

4. Calculate that:
\[
2.273 \times 10^5 \times 2525 = 5.732425 \times 10^8 \text{ bacteria}
\]

5. Converting \( 5.732425 \times 10^8 \) to scientific notation:
\[
5.732425 \approx 5.73 \quad \Rightarrow \quad 5.73 \times 10^8
\]

So, the total number of bacteria in a 2525-gram sample is approximately \( 5.73 \times 10^8 \) bacteria.

**Final Answer:** \( 5.73 \times 10^8 \) bacteria in a 2525-gram sample.