round

round, in music, a perpetual canon on a tune that returns to its beginning in which all the voices enter at the unison or the octave. An example is Sumer Is Icumen In. Rounds were popular in 17th-century England when the catch reached its height. The catch was originally just a simple round, e.g., Three Blind Mice, written in a single line with the effect gained by having another singer come in ("make the catch") at the right time. Later, comic effects, often quite bawdy, were added, using the interweaving of the parts. The Rounds, Catches and Canons of England (1864) by E. F. Rimbault is a comprehensive collection. The term round was also used to designate a dance performed in a circle and, by extension, to the tunes for such dances.

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To eliminate rightmost digits in a number when absolute precision is not required or used. One of the most common uses of rounding is with dollar amounts, which can result in more than two decimal places after a division. Following are four of many rounding methods:

  Round Half Up    3.455 -> 3.46
                   3.454 -> 3.45

  Round Half Down  3.455 -> 3.45
                   3.456 -> 3.46

  Round Up         3.456 -> 3.46
                   3.453 -> 3.46

  Round Down       3.458 -> 3.45
                   3.453 -> 3.45

Rounding and a Lot More

For more ways to round numbers than you can imagine, as well as to learn how computers perform mathematical functions at the circuit level, read the entertaining and informative book, "How Computers Do Math" by Clive "Max" Maxfield and Alvin Brown. (John Wiley & Sons, Inc. 2005, ISBN 0-471-73278-8).