Define Dimensional Analysis.

1.	Define Dimensional Analysis.
Answer» Solution :Often while calculating, there is a need to CONVERT units from one SYSTEM to other. The method used to accomplish this is called factor label method or UNIT factor method or dimensional analysis. e.g., A piece of metal is 3 inch long. What is its length in cm ? We know that 1 in `=2.54` cm From this equivalence, we can write `(1 "in")/(2.54 cm) = 1= (2.54 cm)/(1 "in")` Thus, `(1"in")/(2.54 cm) = 1 ` and `(2.54 cm)/(1 "in")=1` Thus, both of these are called unit factors. If some numberis multipled by these unit factors (i.e. 1), it will not beaffected otherwise. Say, the 3 in given above is multiplied by the unit factor So, `3 " in" = 3 "in" xx(2.54 cm)/(1"in ")=7.62 cm` e.g., A jug contains 2L of milk. Calculate the value of the milk in `m^(3)`. Since `1L = 1000 cm^(3)` and `1m = 100` cm which gives `(1m)/(100 cm) = 1 =(100 cm)/(1m)` To get `m^(3)` from the above unit factors, the first unit factor is TAKEN and it is cubed. `((1m)/(100 cm))^(3)RARR (1m^(3))/(10^(6)cm^(3))=(1)^(3)=1` Now `2L=2 xx 1000 cm^(3)` The above is multiplied by the unit factor `2xx1000 cm^(3) xx (1m^(3))/(10^(6)cm^(3))=(2m^(3))/(10^(3))=2xx10^(-3)m^(3)`

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