Easy Notes Of Physical World And Measurement

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Significant figures: - The significant figures are normally those digits in a measured quantity which are known reliably plus one additional digit that is uncertain.

For counting of the significant figure rule are as:

All non- zero digits are significant figure.

All zero between two non-zero digits are significant figure.
All zeros to the right of a non-zero digit but to the left of an understood

decimal point are not significant. But such zeros are significant if they come from a measurement.

All zeros to the right of a non-zero digit but to the left of a decimal point are significant.

All zeros to the right of a decimal point are significant.

All zeros to the right of a decimal point but to the left of a non-zero digit are not significant. Single zero conventionally placed to the left of the decimal point is not significant.

The number of significant figures does not depend on the system of units.

 In addition or subtraction, the result should be reported to the same number of decimal places as that of the number with minimum number of decimal places. 

 In multiplication or division, the result should be reported to the same number of significant figures as that of the number with minimum of significant figures.

Accuracy refers to the closeness of a measurement to the true value of the physical quantity and precision refers to the resolution or the limit to which the quantity is measured.

 Difference between measured value and true value of a quantity represents error of measurement.

It gives an indication of the limits within which the true value may lie. 

Mean of n measurements

amean page21image5296 

Absolute error ( Δa ) = amean - ai Where ai = measured value It may be - positive, negative or zero.

(i) Mean absolute error

(ii) Relative error - it is the ratio of the mean absolute error to the true value.

δa = I Δa I/ amean


(iii) The relative error expressed in percent is called percentage error.

The error is communicated in different mathematical operations as detailed below: 

 

x = (a ± b), 

Δx = ± ( Δa + Δb)

x = a x b ,

Δx/x = ± ( Δa/a + Δb/b)

x = a/b , 

Δx/x = ± ( Δa/a + Δb/b)

x= anbm /c

Δx/x = ± ( nΔa/a +m Δb/b + pΔc/c

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