Example 12.9 - 7.06 = 5.84 or 5.8 ( rounding off to lowest number of decimal places of original number ).
2 . The relative error of a value of number specified to significant figures depends not only on n but also on the number itself .
Example , accuracy for two numbers 1.02 and 9.89 is ± 0.01 . But relative errors will be :
For 1.02 , (± 0.01 / 1.02 ) x 100 % = ± 1 % For 9.89 , (± 0.01 / 9.89 ) x 100 % = ± 0.1 % Hence , the relative error depends upon number itself .
3 . Intermediate results in multi-step computation should be calculated to one more significant figure in every measurement than the number of digits in the least precise measurement .
Example : 1 / 9.58 = 0.1044 Now , 1 / 0.104 = 9.56 and 1 / 0.1044 = 9.58
Hence , taking one extra digit gives more precise results and reduces rounding off errors .
Dimensions of a Physical Quantity
Dimensions of a physical quantity are powers ( exponents ) to which base quantities are raised to represent that quantity . They are represented by square brackets around the quantity .
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Dimensions of the 7 base quantities are – Length [ L ], Mass [ M ], time [ T ], electric current [ A ], thermodynamic temperature [ K ], luminous intensity [ cd ] and amount of substance [ mol ].
Examples , Volume = Length x Breadth x Height = [ L ] x [ L ] x [ L ] = [ L ] 3 = [ L 3 ] Force = Mass x Acceleration = [ M ][ L ]/[ T ] 2 = [ MLT -2 ] o
The other dimensions for a quantity are always 0 . For example , for volume only length has 3 dimensions but the mass , time etc have 0 dimensions . Zero dimension is represented by superscript 0 like [ M 0 ].
Dimensions do not take into account the magnitude of a quantity