Introduction
In practical use, an engineer would finally obtain result in a numerical form for example, for a set of tabulated data derived from an experiment, inferences may have to be drawn: or, a system of linear algebraic equations is to be solved.
The aim of the Numerical Analysis is to provide efficient methods for obtaining numerical answers to such problems.
Rounding off
In Numerical computations, we come across numbers which have large number of digits and it will be necessary to cut them to a usable number of figures. This process is called Rounding off.
It is usual to round off numbers according to the following rules.
To round off number to n significant digits, discard all digit to the right of the nth digit, and if this discard number is-1] Less than half a unit in the nth place, leave the nth digit unaltered.
2] Greater than half a unit in the nth place, increase the nth digit by unity.
3] Exactly half a unit in the nth place, increase the nthdigit by unity if it is odd: otherwise, leave it unchanged.
The number thus rounded off said to be correct to n significant figures.
Examples on Rounding off :-
Q.) The number given below are rounded-off to four significant figures.
i) 1.6571
ii) 40.0567
iii) 0.759378
iv) 4.14159
Ans: The given number are rounded-off into four significant figure are:
i) 1.6571 to 1.657
ii) 40.0567 to 40.06iii) 0.759378 to 0.7594
iv) 4.14159 to 4.142
Q.) Round-off the following numbers to two decimal places.
46.21416, 2.3742, 22.266, 2.385, 2.385, 71.255
Ans: i) 46.21416 to 46.21
ii) 2.3742 to 2.37
iii) 22.266 to 22.26
iv) 2.385 to 2.38
v) 71.255 to 71.26
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