2.5 x 10^6 bacteria are measured to be in a dirt sample that weighs 1 gram. Use scientific notation to express the number of bacteria that would be in a sample weighing 25 grams.

Answer 1

To find the number of bacteria in a sample weighing 25 grams, you can use a simple proportion based on the number of bacteria per gram.

Given:

• 2.5 x 10^6 bacteria per 1 gram

For a sample weighing 25 grams, you can calculate the total number of bacteria as follows:

\[ \text{Total bacteria in 25 grams} = (\text{bacteria per gram}) \times (\text{weight in grams}) \] \[ \text{Total bacteria in 25 grams} = (2.5 \times 10^6) \times 25 \]

Now, calculate \(2.5 \times 25\):

\[ 2.5 \times 25 = 62.5 \]

Now, we can express \(62.5\) in scientific notation. Since \(62.5 = 6.25 \times 10^1\), we have:

\[ 62.5 \times 10^6 = 6.25 \times 10^1 \times 10^6 = 6.25 \times 10^{7} \]

Thus, the total number of bacteria in a 25-gram sample is:

\[ \text{Total bacteria} = 6.25 \times 10^7 \]

So, the number of bacteria in a sample weighing 25 grams is \(6.25 \times 10^7\).