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:

$$\boxed{{\displaystyle 9.2\times {10}^6}}$$