Errors and Approximation in Physics

Physics is the study of nature and measurement of the physical quantities is vital part of its study. During the measurements of physical quantities errors do occur and here we are dealing with different kind of errors possible.

Accuracy and precision :


The numerical values obtained on measuring physical quantities depend upon the measuring instruments, methods of measurement.

A unit of measurement of a physical quantity is the standard reference of the same physical quantity which is used for comparison of the given physical quantity.

Accuracy refers to how closely a measured value agrees with the true values.

Precision refers to what limit or resolution the given physical quantity can be measured.

Types of Errors:

Uncertainty in measurement of a physical quantity is called the error in measurement.

The difference between the measured value and true value as per standard method without mistakes is called the error.

Error = True value Measured value
Correction = -error

True value means, standard value free of mistakes.

Errors are broadly classified into 3 types :

i) Systematic errors
ii) Random errors
iii) Gross errors

SYSTEMATIC ERRORS :

The errors due to a definite cause and which follow a particular rule are called systematic errors. They always occur in one direction.

Constant error :

Systematic errors with a constant magnitude are called constant errors. The constant arised due to imperfect design, zero error in the instrument or any other such defects. These are also called instrumental errors.

Zero error :

The error due to improper designing and construction.
Ex: If a screw gauge has a zero error of -4 head scale divisions, then every reading will be 0.004cm less than the true value.

Environmental Error:

The error arise due to external conditions like changes in environment, changes in temperature, pressure, humidity etc.
Ex: Due to rise in temperature a scale gets expanded and this results in error in measuring length.

Imperfection in Experimental technique or Procedure:

The error due to experimental arrangement, procedure followed and experimental techniques called Imperfection error.
Ex: In colorimetric experiments, the loss of heat due to radiation, the effect on weighing due to buoyancy of air cannot be avoided.

Personal errors or observational errors:

These errors are entirely due to personal peculiarities like individual bias, lack of proper settings of the apparatus, carelessness in taking observations.
Ex: Parallax error

You may be interested in having a look at units and dimensions concept here below

Units and Dimensions part one and two
Uses and limitations of dimensional formulas
List of dimensional formulas part one and two


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