physics units and measurement

Question

In the study of physics, we often have to measure the physical quantities. The numerical value of a measured physical quantity can only be approximate value as it depends upon the least count of the measuring instrument used. The number of significant figures in any measurement indicates the degree of precision of that measurement. The importance of significant figures lies in calculation. A mathematical calculation cannot increase the precision of a physical measurement. Therefore, the number of significant figures in the sum or product of a group of numbers cannot be greater than the number that has the least number of significant figures because a chain cannot be stronger than its weakest link. The difference in the true value and the measured value of a quantity is the measure of error in the measurement.                                        

(a) What are significant figures?
( b) Define least count.
(c) Is there any relation between precision and accuracy?
(d)State the relation between significant figures and precision.
(e) How systematic errors can be minimized?

Answer 1

(a) The term “significant figures” refers to the number of important single digits (0 to 9 inclusive) in the coefficient of expression in the scientific notation.

(b) The least count of an instrument is the smallest measurement that can be taken accurately with it.

(c) The difference between precision and accuracy is given below

Precision

(1) It could be defined as the level of correctness of a measurement to its true value.

(2) It has one factor used for measuring.

(3) Accurate items have to be precise in most cases.

Accuracy

(1) It could be defined as the sharp exactness of a measurement.

(2) It has multiple factors for measurement.

(3) Precise items may or may not be accurate.

(d) The smaller the measurement increment, the more precise the tool. Significant figures express the precision of a measuring tool. When multiplying or dividing measured values, the final answer can contain only as many significant figures as the least precise value.

(e) Systematic errors can be minimized by improving experimental techniques, selecting better instruments and removing personal bias as far as possible. For a given set up, these errors may be estimated to a certain extent and the necessary corrections may be applied to the readings.