Rounded - SpeedyLook encyclopedia

Current method to round (Round-off with nearest or arithmetic round-off)

Let us give here the stages of this method

to choose the figure which will be the last to be preserved.
to increase this figure by a unit if the following figure is worth at least 5 (this calls rounding by excesses)
to leave it identical if the following figure is strictly lower than 5 (that is called the rounding by defect)

Example: 3,046 can be round with the hundredths into 3,05 (because the following figure (6) is higher than 5).

Other examples by keeping one figure after the comma:

1,349 becomes 1,3 (because the figure following 3 is strictly lower than 5)
1,350 becomes 1,4 (because the figure following 3 is worth at least 5)

In fact the method consists in separating the ten decimal digits (0,1… 9) in two parts:

5 first: 0,1,2,3 and 4 for which one reaches the lower value
the 5 following: 5,6,7,8 and 9 for which one reaches the higher value

This method limits the accumulation of errors during successive calculations.

Method of rounding to the par nearest

If four (or a lower figure) is the figure which follows the decimal to which the number must be round, then the decimal remains unchanged. Whereas if the figure following the decimal is six or more, the decimal is increased by a unit. Finally if the following figure is the figure five itself followed by figures different from zero, then the decimal is increased by a unit, while if five is followed of no figure (or that by zeros) then the decimal is increased by a unit when it is odd and remains unchanged if not. This method is sometimes called “rounded with the even figure” and is employed in order to eliminate the Biais which would occur by rounding each time by excess the numbers whose last figure is five.

Examples:

3,046 round-offs with the hundredths becomes 3,05 (because the following figure (6) is higher than 6)
3,043 round-offs with the hundredths becomes 3,04 (because the following figure (3) is lower than 4)
3,045 round-offs with the hundredths becomes 3,04 (because the last figure is 5, and the preceding figure (4) is even)
3,015 round-offs with the hundredths becomes 3,02 (because the last figure is 5, and the preceding figure (1) is odd)

This method is also named " rounded bancaire".

For a rounding with the entirety nearest, see the whole function left.

Other methods

Other methods round various manners:

by lowering to Zero decimals (also known under the name of Truncation),
while rounding with the greatest lower entirety (whole function left),
while rounding with the smallest higher entirety (left whole by excess).

Also see

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