Question

A small paper clip has a mass of about 1 gram. The paper clip has how many times the mass of the $4.8\times {{10}^{8}}E$. coli bacteria?

Answer 1

Hint: Firstly, we will use the experimental data from the study of the coli bacteria which states that each Escherichia coli bacteria has a mass of about $2\times {{10}^{-12}}g$. Then, we use another fact that after 30 hrs, the number of bacteria in the pool becomes $4\times {{10}^{8}}$. Then, we find the mass of the total population of bacteria by multiplying the terms $2\times {{10}^{-12}}g$ and $4\times {{10}^{8}}$. Then, to find the paper clip has how many times the mass of the $4.8\times {{10}^{8}}E$. coli bacteria, divide the mass of the total population calculated above which is $9.6\times {{10}^{-4}}g$ to the mass asked for the bacteria which is 1g.

Complete step-by-step solution
In this question, we will use the experimental data from the study of the coli bacteria which states that each Escherichia coli bacteria has a mass of about:
$2\times {{10}^{-12}}g$
Now, we also know from the study that after 30 hrs, the number of bacteria in the pool becomes:
$4\times {{10}^{8}}$
Then, find the mass of the total population of bacteria after 30 hrs is calculated by multiplying the terms $2\times {{10}^{-12}}g$ and $4\times {{10}^{8}}$. So, the result of the multiplication is:
$2\times {{10}^{-12}}\times 4.8\times {{10}^{8}}g=9.6\times {{10}^{-4}}g$
Now, it is given in the question that the mass of the small paper clip is 1g.
To get the number of the times the mass to paper clip is the mass of the $4\times {{10}^{8}}E$ coli bacteria, divide the mass of the total population calculated above which is $9.6\times {{10}^{-4}}g$ to the mass asked for the bacteria which is 1g.
Now, perform the division and we get:
$\dfrac{9.6\times {{10}^{-4}}g}{1g}=9.6\times {{10}^{-4}}$
Hence, the paper clip is $9.6\times {{10}^{-4}}$ times the mass of the $4.8\times {{10}^{8}}E$. coli bacteria.

Note: The question contains experimental data from the study of the Escherichia coli bacteria. So, it is necessary to take all the values very carefully from that study to get the accurate result of the question. Take the mass of the Escherichia coli bacteria as $2\times {{10}^{-12}}g$ and from the study that after 30 hrs, the number of the bacteria becomes in water is $4\times {{10}^{8}}$.