Question

The size of bacteria is \[1\mu \] . Find the number of bacteria in \[1m\] length.
(A). \[{{10}^{3}}\]
(B). \[{{10}^{6}}\]
(C). \[{{10}^{4}}\]
(D). \[{{10}^{5}}\]

Answer 1

Hint: To calculate the number of bacteria, determine how many parts of micron is equivalent to a meter in the metric system. Since the size of one bacterium is \[1\mu \] , by the unitary method, the number of parts of micron in a meter will be equal to the number of bacteria in a meter.

Formula used:
 \[1\mu ={{10}^{-6}}m\]

Complete step by step solution:
One micron ( \[1\mu \] ) is one of the measurements of particle size. It is equal to one-millionth part of a metre.
 \[1\mu ={{10}^{-6}}m\] - (2)
Bacteria are unicellular microorganisms that live in different types of environments. The size of bacteria is given to be 1 micron.
Therefore we can say that there is 1 bacterium in \[1\mu m\]
From eq (1)
 \[\begin{align}
  & 1\mu ={{10}^{-6}}m \\
 & \Rightarrow {{10}^{6}}\mu =1m \\
 & \\
\end{align}\]
From the above eq. we can conclude that there are \[{{10}^{6}}\mu \] in \[1m\] .
Since \[{{10}^{6}}\] is the size of 1 bacterium. So there are \[{{10}^{6}}\] bacteria in \[1m\] .

So, the correct answer is “Option B”.

Additional Information: Unitary method is a math technique that is used to find the value for one and use to find required value for a given number or find a number from a given value.
For example-Let the price of 1 pen be x, then the price of 10 pens is \[10x\] .
If the price for 5 apples is \[y\] , the price for one apple is \[\dfrac{y}{5}\] .

Note: The sizes of bacteria can range from as small as \[0.3\mu \] to as large as \[0.7mm\] . Bacteria are unicellular which means that they are made up of a single cell and a single cell performs all the life functions necessary for existence. In bacteriology, micron is the primary unit of measurement.