Friday, December 15

How To Round Off Calculations?

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The result of computation with approximate numbers, which contain more than one uncertain digit, should be rounded off.

While rounding off measurements, we use the following rules by convention:

Rule 1. If the digit to be dropped is more than 5, then the preceding digit is raised by one  For example, x=6.87 is rounded off to 6.9.  Again, x=12.78 is rounded off to 12.8.

Rule 2. If the digit to be dropped is less than 5, then the preceding digit is left unchanged.  For example, x=7.82 is rounded off to 7.8  Again, x=3.94 is rounded off to 3.9.

Rule 3. If the digit to be dropped is 5 followed by digits other than zero, then the preceding digit is raised by one.

For example, x=16.351 is rounded off to 16.4.  Again x=6.758 is rounded off to 6.8.

Rule 4. if the digit to be dropped is 5 or 5 followed by zeros, then the preceding digit is left unchanged, if it is even.

For example, x=3.250 becomes 3.2 on rounding off.  Again x=12.650 becomes 12.6 on rounding off.

Rule 5. If the digit to be dropped is 5 or 5 followed by zeros, then the preceding digit is raised by one, if it is odd.

For example, x=3.750 is rounded off to 3.8.  Again, x=16.150 is rounded off to 16.2.

Note 1. For calculation, a number known accurately to many significant digits can be rounded off to an approximate value.  For example, speed of light in vacuum is c=2.99792458 x 108 m/s.  it is rounded off to c=3 x 108 m/s.

2. The value of pi=3.1415926 is known to a large number of significant figures.  However, in calculations, we may take pi=3.142 or 3.14, as per our requirement.

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