Question

The photograph of a bacteria enlarged 50,000 times attains a length of 5 em as shown below. What is the actual length of the bacteria? What is the length when it is enlarged 20,000 times only?

Answer 1

Hint: In order to solve this question, one should know the conversion value of em to metre. It is given by, 1 em = 0.00421 m. We will find the length of the actual bacteria by dividing 5em by 50,000 and then we will find the length of the bacteria when it is enlarged 20,000 times by multiplying the actual length with 20,000.

Complete step-by-step answer:
It is given in the question that the length of bacteria enlarged 50,000 times is 5 em. So, we can say that the actual length of bacteria, that is the length of the bacteria when it is not enlarged. So, we can write,
$\dfrac{5}{50000}=\dfrac{1}{10000}=\dfrac{1}{{{10}^{4}}}={{10}^{-4}}em$
Now, we will convert em to meter, so we know that 1 em = 0.00421 m. So, can write,
$\begin{align}
  & {{10}^{-4}}em={{10}^{-4}}\times 0.00421m \\
 & =4.21\times {{10}^{-7}}m \\
\end{align}$
Therefore, we get the actual length of the bacteria as $4.21\times {{10}^{-7}}m$.
Now, we will find the length of the bacteria when it is enlarged 20,000 times is. We have found out the actual length of the bacteria as $4.21\times {{10}^{-7}}m$, so in order to find the length of the bacteria when it is enlarged 20,000 times, we will multiply it with the actual length of the bacteria. So, we can write,
$\begin{align}
  & 4.21\times {{10}^{-7}}\times 20000 \\
 & =8.42\times {{10}^{-3}}m \\
\end{align}$
We can also write the length in em, so we get,
$8.42\times {{10}^{-3}}\times \dfrac{1}{0.00421}=2em$
Therefore, we get the length of the bacteria when it is enlarged 20,000 times as $8.42\times {{10}^{-3}}m$ or 2 em.

Note: To find the length of bacteria which is 20000 times enlarged, we can also directly multiply 5 em by $\dfrac{2}{5}$ which gives us 2 em, and that is the required answer. Most of the students get confused while finding the actual length and perform multiplication of 5 and 50,000 instead of division and this will lead to the wrong answers.