Friday, December 15

# How To Round Off Calculations?

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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