. g. The relative error in . g is = (± .
/ . ) × % = ± % Similarly, the relative error in . g is = (± . / .
) × % = ± . % Finally, remember that intermediate results in a multi-step computation should be calculated to one more significant figure in every measurement than the number of digits in the least precise measurement. These should be justified by the data and then the arithmetic operations may be carried out; otherwise rounding errors can build up. For example, the reciprocal of .
, calculated (after rounding off) to the same number of significant figures (three) is . , but the reciprocal of . calculated to three significant figures is . .
However, if we had written / . = . and then taken the reciprocal to three significant figures, we would have retrieved the original value of . .
This example justifies the idea to retain one more extra digit (than the number of digits in the least precise measurement) in intermediate steps of the complex multi-step calculations in order to avoid additional errors in the process of rounding off the numbers. . DIMENSIONS OF PHYSICAL Q UANTITIES The nature of a physical quantity is described by its dimensions. All the physical quantities represented by derived units can be expressed in terms of some combination of seven fundamental or base quantities.
We shall call these base quantities as the seven dimensions of the physical world, which are denoted with square brackets [ ]. Thus, length has the dimension [L], mass [M], time [T], electric current [A], thermodynamic temperature [K], luminous intensity [cd], and amount of substance [mol]. The dimensions of a physical quantity are the powers (or exponents) to which the base quantities are raised to represent that quantity . Note that using the square brackets [ ] round a quantity means that we are dealing with ‘ the dimensions of ’ the quantity.
In mechanics, all the physical quantities can be written in terms of the dimensions [L], [M] and [T]. For example, the volume occupied by an object is expressed