Question

Which of the following measurements is most precise?
A. 4.00 mm
B. 4.00 cm
C. 4.00 m
D. 40.00 m

Answer 1

Hint: A measurement which has a lesser value of absolute error is more precise.

Complete step by step answer:
A measurement is said to be more accurate when it has a lesser value of relative error. However, a measurement is said to be more precise when it has a lesser value of absolute error, that is, it is measured by an instrument that has a smaller least count.
For a measurement x, the relative error is given by
$\dfrac{\left| \Delta x \right|}{x}$
And the absolute error is given by
$\left| \Delta x \right|$

In the given options, it is clear that the relative error in options A), B) and C) are the same, that is $\dfrac{0.01}{4}=0.0025$ . However, in option D) the relative error is $\dfrac{0.01}{40}=0.00025$. Therefore, option D) is the most accurate measurement.
On the other hand, it is clear that the measurement in option A) has been made with an instrument with the minimum least count (0.01 mm) in comparison to the other options. Thus, the absolute error in measure of option A) is 0.01 mm, which is the least in comparison to the other options.
Therefore, 4.00 mm is the most precise measurement.
Thus, the correct option is A) 4.00 mm.

Note: Students may get confused between accuracy and precision and make a mistake. This is quite a tricky topic in general. However, if practised well, it can be very easy and fetch easy extra marks, especially in competitive exams. In this way the student can have an edge over others, because most students neglect this topic. However, it forms the basics of learning physics and other science subjects in general.