Question

8.6 × 10^7 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 19 grams. answer attempt 1 out of 2 answer: × 10 bacteria

Explanation:

Step1: Set up the proportion

If 1 gram of dirt has $8.6\times 10^{7}$ bacteria, then for a 19 - gram sample, we multiply the number of bacteria per gram by the number of grams. So the number of bacteria $N=(8.6\times 10^{7})\times19$.

Step2: Calculate the product

First, calculate $8.6\times19 = 163.4$. Then, $N = 163.4\times10^{7}$.

Step3: Convert to proper scientific - notation

In scientific notation, a number is written as $a\times 10^{n}$ where $1\leqslant a<10$. We rewrite $163.4\times10^{7}$ as $1.634\times10^{2}\times10^{7}$. Using the rule of exponents $a^{m}\times a^{n}=a^{m + n}$, we get $1.634\times10^{2 + 7}=1.634\times10^{9}$.

Answer:

$1.634\times 10^{9}$ bacteria