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