Question

Which of the following readings taken by microscope of least count of $0.001$ cm is correct?
(A) $3.28$
(B) $3.00$
(C) $3.000$
(D) $0.02345$

Answer 1

Hint: The travelling microscope is divided into two halves and there are $50$ divisions on the Vernier scale. The least count of travelling microscopes is $0.001$ cm. Least count is the smallest value up to which an instrument can measure. If the scale can measure up to three values after the decimal then all the readings of the microscope will have three values after the decimal.

Complete step by step solution: A microscope or traveling microscope is a measuring device used to measure the length up to three places after the decimal accurately.
The least count of microscope is calculated as follows:
The travelling microscope which is usually used has each millimeter divided into two equal halves. The smallest division on the main scale will be $0.5$ millimeter (mm). As there are $50$ divisions on the Vernier caliper scale therefore, the least count of travelling microscopes will be $\dfrac{{0.5}}{{50}} = 0.001$ mm.
As there are three values after the decimal therefore, the measured value must also have three values after the decimal.
The given readings are:
$3.28$ , as it has only two values after the decimal hence, option A is not the correct option.
$3.00$ , in this measure value there are only two decimal values hence, option B is also incorrect.
$3.000$ as there are three values after decimal hence, option C is the correct option.
$0.02345$ there are five values after the decimal hence, option D is also incorrect.

So, only option C is the correct option.

Note: The least reading is the minimum length a scale can measure. In our day to day used ruler, the Least count is $0.1\,mm$ . Therefore, any length measured using the regular value will have only one decimal value. For a microscope, it has three decimal values.