9.2 x 10^5 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 10 grams.

Answer 1

To find the number of bacteria in a 10-gram sample, you can use the given measurement of 9.2 x 10^5 bacteria in a 1-gram sample.

If there are 9.2 x 10^5 bacteria in 1 gram, then in 10 grams, you multiply the number of bacteria by 10:

\[ 9.2 \times 10^5 \text{ bacteria/gram} \times 10 \text{ grams} = 9.2 \times 10^5 \times 10^1 \]

Now, since \(10 = 10^1\), you can add the exponents:

\[ 9.2 \times 10^{5 + 1} = 9.2 \times 10^6 \]

Thus, the number of bacteria in a 10-gram sample is:

\[ \boxed{9.2 \times 10^6} \]