Question

There are 20 million bacteria per square centimeter of coral in a coral reef. The coral reef covers 13000 km^2. How many bacteria are there in the coral reef?

Answer 1

Answer:

2.6 * $10^{21}$ bacteria

Step-by-step explanation:

We know that there are 20 million bacteria in 1 $cm^2$ of coral reef. Let's write the number of bacteria in scientific notation with powers of 10:

$20,000,000= 2*10^7$

Now let's write 1 $cm^2$ in square meters, knowing that one cm equal 0.01 meter ($10^{-2}$ meters:

$1 \, cm^2 = 1* (10^{-2}\,m)^2= 10^{-4}\, m^2$

So now we can find how many bacteria there is in one $m^2$ of coral reef:

Number of bacteria in $1\,m^2 = 2 * 10^7* 10^4 = 2 * 10^{11}$ bacteria

we can now express 13000 $km^2$ in $m^2$ knowing that 1 km = 1000 m = $10^3$ m:

$13000\,km^2= 1.3 * 10^4 \,km^2=1.3 * 10^4*(10^3m)^2= 1.3*10^4*10^6\'m^2=$

Since we know the number of bacteria per every $m^2$ of coral reef, the number of bacteria in $1.3*10^{10}\,m^2$ of coral reef will be the product of these two numbers:

Total number of bacteria: $2*10^{11} * 1.3*10^{10}=2.6* 10^{21}$