Accuracy Of Numbers
Accuracy Of Numbers
1. Approximate Numbers :
There are two types of numbers exact and approximate . Exact numbers are 2,4,9,13,7,2,6.45....etc . But there are numbers such as 4/3 =1.3333.... , √(2)= 1.41413 and finite number of digits . These may be approximated by numbers 1.3333, 1.4141 , 3.1416 respectively . Such numbers which represent the given numbers to certain degree of accuracy are called approximate numbers .
2. Significant Figures :
The digits used to express a number is called significant digits (figures) . Thus each of the numbers 7845, 3.589, 0.4758 contains four significant figures while the numbers 0.00389 , 0.000587 and 0.0000296 contain only three significant figures since zeros only help to fix the position of the decimal point . Similarly the numbers 45000 and 7300.00 have two significant figures only .
3. Rounding Off :
There are numbers with large number of digits e.g 23/7 = 3.2757142 . In practice , it is desirable to limit such numbers to a manageable number of digits is called rounding off . Numbers are rounded cutting off unwanted digits is called rounding off . Numbers are rounded off to cause the least possible errors .
Rules to round off a number to n significant figures :
(i) Discard all digits to the right of the nth digit .
(ii) If this discarded number is
(a) less than half a unit in the nth place , leave the nth digit unchanged .
(b) greater than half a unit in the nth place increase the nth digit by unity .
(c) exactly half a unit in the nth place increase the nth digit by unity if it is odd otherwise leave it unchanged .
For instance , the following numbers rounded off to three significant figures are :
7.893 to 7.89 3.567 to 3.57
12.865 to 12.9 84.767 to 84.800
6.4356 to 6.44 5.8254 to 5.82
Also the numbers 6.284359 , 9.864651, 12 . 464762 rounded off to four places of decimal at 6.2844 , 9.8646 , 12.4686 respectively .
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