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What points to be considered during multiplication and division of significant numbers ? |
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Answer» Solution :For different types of SIGNIFICANT numbers in multiplication and division following points should be followed : (1) In multiplication or in division the final result should retain as many significant as there are in the original number with leastsignificant (2) When two number are to be multiplied or divided and out of them which is not a measurement is a definite number, the integers and fraction that occur in general in physical equations are definite number. For EXAMPLE, (1) Length and breadth of a PLATE are 1.567 cm and 10.4 cm RESPECTIVELY then AREA of plate `1.567 xx 10.4 = 16.2968 cm^(2)` But `10.4` represent number with 3 significant digit (minimum) hence area of plate should be rounded off to`=16.3 cm^(2)` (2) Let mass of an object is 8.254g and volume is `2.68 cm^(3)` `"Density"=("mass")/("volume")` `=(8.254)/(2.68)` `=3.07895074626 gcm^(-3)` The number 2.68 is with 3 significant digit hence result also should be represented with 3 significant digit hence it will be `3.08 g cm^(-3)` (3)If any number used in calculation have many infinite) significant figure then it should be rounded off to finite significant digit during calculation as per requirement in specific cases. (4) In any equation constant like `pi, epsi_(0) mu_(0), eta` are part of equation, then it should be rounded off to one digit more than given significant number For example, `pi` = 3.1415926 then depending on requirement of calculation it should be rounded off to 3.14, 3.142, 3.1416 while using calculation. |
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