3.4 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 9 grams.

Answer 1

To find the number of bacteria in a sample that weighs 9 grams, we can use a simple multiplication based on the initial measurement of 3.4 x 10^5 bacteria per gram.

1. First, we multiply the number of bacteria in 1 gram by the weight of the new sample (9 grams):

$$3.4\times {10}^5\text{ bacteria/gram}\times 9\text{ grams}=30.6\times {10}^5\text{ bacteria}$$

2. Next, we convert $30.6\times {10}^5$ into scientific notation. To do this, we need to adjust it so that there's only one non-zero digit to the left of the decimal:

$$30.6\times {10}^5=3.06\times {10}^6$$

Hence, the number of bacteria in a 9 gram sample is:

$$\boxed{{\displaystyle 3.06\times {10}^6}}$$