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.

Read more about Rounding:  Types of Rounding, Rounding To A Specified Increment, Rounding To Integer, Tie-breaking, Dithering and Error Diffusion, Rounding To Simple Fractions, Scaled Rounding, Round To Available Value, Floating-point Rounding, Double Rounding, Exact Computation With Rounded Arithmetic, The Table-maker's Dilemma, History, Rounding Functions in Programming Languages

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)