Question

Four students measure a time interval that is known to be \[1.734s\]. The measurement recorded by each student is shown. Which measurement is the most accurate?
$\left( A \right) 1s$
$\left( B \right) 1.7s$
$\left( C \right) 1.83s$
$\left( D \right) 1.604s$

Answer 1

Hint: The measure of the closeness of the measured value to the true value is called accuracy. The preceding digit is unchanged if the immediate digit is less than five. The preceding number raised by one of the immediate digits is greater than five. Now by using the above statement we can find the most accurate number. The smaller the uncertainty in the measured value greater is the accuracy.

Complete step by step answer:
Accurate measurements of physical quantities play a very important role in the field of physics. We can completely understand physical quantities if we are able to measure it. The measure of the closeness of the measured value to the true value is called accuracy. The smaller the uncertainty in the measured value greater is the accuracy.

Accuracy depends on the resolution of an instrument. Measurement will be accurate if we use a precise instrument. For example, let us consider the length of the rod to $1.58cm$. The first instrument measures $1.5cm$. Another instrument measures it as $1.45cm$. Now by comparing the two we can say the first value $1.5cm$ is the more accurate value.

Errors could be because of several reasons both controllable and uncontrollable. Hence to interpret the result and evaluate the result the knowledge of errors is required.
In the same way here the time interval is given as $1.734s$.

From the given options the most accurate value is $1.7s$ because it is the closest to the true value.

Note: Despite great achievements and sophistication in the development of instruments, no measurement is free from error. The measure of the closeness of the measured value to the true value is called accuracy. Accuracy depends on the resolution of an instrument. The smaller the uncertainty in the measured value greater is the accuracy. Precision tells us the limit of the quantity measured.