Question

there are 30 million bacteria per square centimeter of coral in a coral reef. the coral reef covers 16,000 km². how many bacteria are there in the coral reef?

Explanation:

Step1: Convert area units

First, convert $16000\ km^{2}$ to $cm^{2}$. Since $1\ km = 100000\ cm$, then $1\ km^{2}=(100000)^{2}\ cm^{2}= 10^{10}\ cm^{2}$, so $16000\ km^{2}=16000\times10^{10}\ cm^{2}=1.6\times 10^{14}\ cm^{2}$.

Step2: Calculate number of bacteria

There are 30 million ($30\times10^{6} = 3\times10^{7}$) bacteria per square - centimeter. Multiply the number of bacteria per square - centimeter by the total area of the coral reef in square - centimeters. The number of bacteria $N=(3\times 10^{7})\times(1.6\times 10^{14})$. Using the rule of exponents $a^{m}\times a^{n}=a^{m + n}$, we have $N=(3\times1.6)\times10^{7 + 14}=4.8\times10^{21}$.

Answer:

$4.8\times 10^{21}$