# Rounding

Rounding a numerical value means replacing it by another value that is approximately equal but has a shorter, simpler, or more explicit representation; for example, replacing £23.4476 with £23.45, or the fraction 312/937 with 1/3, or the expression √2 with 1.414.

Rounding is often done on purpose to obtain a value that is easier to write and handle than the original. It may be done also to indicate the accuracy of a computed number; for example, a quantity that was computed as 123,456 but is known to be accurate only to within a few hundred units is better stated as "about 123,500."

On the other hand, rounding introduces some round-off error in the result. Rounding is almost unavoidable in many computations — especially when dividing two numbers in integer or fixed-point arithmetic; when computing mathematical functions such as square roots, logarithms, and sines; or when using a floating point representation with a fixed number of significant digits. In a sequence of calculations, these rounding errors generally accumulate, and in certain ill-conditioned cases they may make the result meaningless.

Accurate rounding of transcendental mathematical functions is difficult because the number of extra digits that need to be calculated to resolve whether to round up or down cannot be known in advance. This problem is known as "the table-maker's dilemma".

Rounding has many similarities to the quantization that occurs when physical quantities must be encoded by numbers or digital signals.

### Other articles related to "rounding":

Other Rounding Standards - Negative Zero in Meteorology
... small is the magnitude for example, when rounding temperatures in the Celsius scale, where below zero indicates freezing ...
Blohm & Voss Ha 140 - Specifications (Ha 140 V2)
... Max takeoff weight 9,230 kg (20,349 lb) Fuel capacity 2,365 l (Bad rounding here520 imp gal) Powerplant 2 × BMW 132K 9-cyl ... air-cooled radial piston engines, 597 kW (801 hp) each for take-off 619 kW (Bad rounding here830 hp) at 1,000 m (Bad rounding here3,300 ft) Propellers 3-bladed ...
Swedish Rounding - Mechanics - Rounding With 50 øre Intervals
... Rounding is only done on the total sum of a purchase, which makes that effect smaller ... In many shops all prices are already rounded to the whole krone, so that no rounding takes place ...
Swedish Rounding - Details
... Rounding becomes necessary where low denomination coins in a currency are withdrawn or otherwise made unavailable, but the currency's subdivisions remain the same ... Since it may not be possible to make exact change for a purchase, rounding the total bill to the lowest available denomination of coinage is required if a customer is paying in cash ... credit card, debit card, EFTPOS or cheque, no rounding is necessary ...
Swedish Rounding
... Swedish rounding is rounding the basic cost of a purchase which is to be paid for in cash to the nearest multiple of the smallest denomination of currency ... The term "Swedish rounding" is used mostly in Australia, where such a method has been practised since the 1990s ...

### Famous quotes containing the word rounding:

The past absconds
With our fortunes just as we were rounding a major
Bend in the swollen river; not to see ahead
Becomes the only predicament when what
Might be sunken there is mentioned only
In crabbed allusions but will be back tomorrow.
John Ashbery (b. 1927)

I look for the new Teacher that shall follow so far those shining laws that he shall see them come full circle; shall see their rounding complete grace; shall see the world to be the mirror of the soul; shall see the identity of the law of gravitation with purity of the heart; and shall show that the Ought, that Duty, is one thing with Science, with Beauty, and with Joy.
Ralph Waldo Emerson (1803–1882)

People forget that it is the eye that makes the horizon, and the rounding mind’s eye which makes this or that man a type or representative of humanity with the name of hero or saint.
Ralph Waldo Emerson (1803–1882)