THEORY OF ERRORS

COMPILED BY ARUP ROY CHOUDHURY, ASSOCIATE PROFESSOR, DEPARTMENT OF MATHEMATICS, MALDA COLLEGE, MALDA

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THEORY OF ERRORS

THEORY OF ERRORS

THEORY OF ERRORS

THEORY OF ERRORS

Example: Let the number 3.257450 be rounded to four decimal places. Then rounding-off the given number to four decimal place is 3.2574. Here exactly 5 is in the 5^th decimal place and 4 is in fourth decimal place which is even. So we keep the 4^th digit from decimal point unaltered and discard all the digits from 5^th decimal place.

Example: We consider the numbers 23.4556, 0.52375, 14.00879, 0.0035845 and round-off the numbers to four significant digits. Here exactly 5 is in the 5^th digit and the fourth digit is odd in first two numbers. So we increase the 4^th digit by 1. Thus the numbers 23.4556 and 0.52375 rounded to 23.46 and 0.5238 respectively.

For the number 14.00879, fifth digit is greater than 5 and so we add 1 to 4^th digit which gives 14.01 as the number rounded-off to four significant digits.

For the number 0.0035845, fifth digit is 5 and 4^th digit is an even number. So we leave the 4^th digit unaltered which gives 0.003584 as the number rounded-off to four significant digits.

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THEORY OF ERRORS

THEORY OF ERRORS

THEORY OF ERRORS

THEORY OF ERRORS

43.52189, 0.04352189, 4352189000, 4352189

Solution:

THEORY OF ERRORS