1.1 Measurement Techniques

Firstly you can watch this video to understand a digital and analog measurement,

Secondly, Physics being an experimental subject has to deal with errors. Generally speaking there are two types of error that comes up in experimental physics,


1. Systematic Error
2. Random Error

There are two other terms associated with those errors: Precision and Accuracy

and two notion of uncertainty,

3. Fractional Uncertainty
4. Percentage Uncertainty

First we discuss on  the Systematic Error,

'Systematic errors in experimental observations usually come from the measuring instruments, in other words faulty measuring instruments gives arise to an error that deviates by a fixed amount from the true value of measurement resulting in measurements taken being faulty in unidirection.'

Here are some examples of random and systematic error.

Secondly the Random Error,
 
'Random errors are caused by unknown and unpredictable changes in the experiment, these changes may occur in the measuring instruments or in the environmental conditions. It leads to measured values being inconsistent when repeated measures of a quantity are taken, this results in a scatter of measured values about a mean value. The errors is in bidirectional either positive or negative about mean value.'

Here are some examples of random and systematic error.

Accuracy: The accuracy of a measurement is a measure of  how close the measurement is to the true value of the quantity being measured. The accuracy of measurements is often reduced by systematic errors, which are difficult to detect even for experienced research workers.

Precision: The precision of a measurement is how close a number of measurements of the same quantity agree with each other. The precision is limited by the random errors. It may usually be determined by repeating the measurements.

Here are some simple examples of accuracy and precision.

Here's a short video for clearer concept:

Fractional Uncertainty: Ratio of uncertainty of the least count to the principle measurement amount to the fractional uncertainty.

Percentage Uncertainty: When you multiply the fractional uncertainty by 100, it becomes the percentage uncertainty.

EX: Find fractional and percentage uncertainty of the following measurement. length=10$\pm$.5m
Soln: fractional uncertainty=.5/10
          percentage uncertainty=5$\%$

Here's is good example of the fractional and percentage uncertainty and some more calculation.

references: umd, university physics