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

2.6 *
`10^(21)` bacteria

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)`