Rounding

From Free net encyclopedia

Rounding means reducing the significant digits in a number while trying to keep its value similar. The result is less accurate, but easier to use.

Example: 73 rounded to the nearest ten is 70, because 73 is closer to 70 than to 80.

Rounding can be analyzed as a form of quantization.

There are several commonly-used rules for rounding off.

1 Common method of rounding
2 Statistician's method of rounding
3 Other methods
4 See also
5 External links

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Common method of rounding

This method is commonly used, for example in accounting.

Decide which is the last digit to keep.
Increase it by 1 if the next digit is 5 or more (this is called rounding up)
Leave it the same if the next digit is less than 5 (this is called rounding down)

Example: 3.046 rounded to hundredths is 3.05 (because the next digit [6] is 5 or more).

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Statistician's method of rounding

If four (or less) is the digit that follows the last digit to be rounded off, then the last reportable digit stays as it was. Whereas, the last reportable digit increases by one if the digit following the digit to be rounded is six or more. If there is a five followed by non-zero digits, it will be increased by one, but if the five is succeeded by nothing, only odd last reportable digits are increased by one, while even last reportable digits stay the same. This method is sometimes known as "round to even" and is used in order to eliminate the bias that would come from always rounding a number ending in five up every time.

Examples:

3.046 rounded to hundredths is 3.05 (because the next digit (6) is 6 or more)
3.043 rounded to hundredths is 3.04 (because the next digit (3) is 4 or less)
3.045 rounded to hundredths is 3.04 (because the last digit is 5, and the next digit (4) is even)
3.015 rounded to hundredths is 3.02 (because the last digit is 5, and the next digit (1) is odd)

For rounding to the nearest integer, see nearest integer function.

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Other methods

Other methods of rounding include round towards zero (also known as truncation), round away from zero, floor (reduce non-round numbers to greatest lesser round number) and ceiling (increase non-round numbers to least greater round number).

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