Question

A photograph of a bacteria enlarged 50,000 times attains a length of 5 cm. What is the actual length of the bacteria? If the photograph is enlarged 20,000 times only, what would be its enlarged length?

Answer 1

Hint: In this question it is given that a photograph of a bacteria enlarged 50,000 times attains a length of 5 cm. We have to find the actual length of the bacteria and also the enlarged length if it is enlarged 20,000 times. So to find the solution we need to use a unitary method, from where we are able to find the length of the bacteria when it enlarged 1 times, so enlarging 1 times is equivalent to the actual length of bacteria.
So before jumping into the solution let us understand, what is a unitary method?
The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value. In essence, this method is used to find the value of a unit from the value of a multiple, and hence the value of a multiple.

Complete step-by-step answer:
Given,
Photograph enlarged 50,000 times attains the length = 5 cm
$\therefore$ Photograph enlarged 1 times attains the length = $$\dfrac{5}{50000} $$cm=$$\dfrac{5}{5\times 10000}$$ cm=$$\dfrac{1}{10000} cm=0.0001\ $$cm
Therefore, the actual length is 0.0001 cm
Now when it enlarged 20,000 times then the length will be $$20000\times 0.0001\ $$cm=2cm


Note: To divide a whole or a decimal number by 10000, move the decimal point four places to the left. Note that although a whole number does not have a decimal point, we can always add it at the end of the number. (For example, 27 and 27. are the same numbers.) Also note that if there are not enough digits to move the decimal point the required number of places, we can always add extra zeros. For example, 1 can be written as 00001, so if we divide 1 by 10000 we have to move the decimal point four places to the left which is 0.0001.