rounding$94004$ - definizione. Che cos'è rounding$94004$
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Cosa (chi) è rounding$94004$ - definizione

REPLACING NUMERICAL VALUE BY ANOTHER APPROXIMATELY EQUAL
Rounding functions; Banker's rounding; Round to even; Nearest integer function; Stochastic rounding; Statistician's rounding; Rounding function; Rounding numbers; Bankers' rounding; Directed rounding; Unbiased rounding; ASTM rounding; Bankers rounding; Table-maker's dilemma; Rounding to integer; Nearest integer; Dutch rounding; Gaussian rounding; Sticky rounding; Sticky round; Round to odd; Rounding to odd; Rounding-to-odd; Round-to-odd; Sticky-round; Double rounding; Round half to even; Rounded number
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Rounding         
·adj Round or nearly round; becoming round; roundish.
II. Rounding ·p.pr. & ·vb.n. of Round.
III. Rounding ·noun Small rope, or strands of rope, or spun yarn, wound round a rope to keep it from chafing;
- called also service.
IV. Rounding ·noun Modifying a speech sound by contraction of the lip opening; labializing; labialization. ·see Guide to Pronunciation, / 11.
Rounding         
Rounding means replacing a number with an approximate value that has a shorter, simpler, or more explicit representation. For example, replacing $ with $, the fraction 312/937 with 1/3, or the expression with .
Cash rounding         
  • Chinese receipt showing the total being truncated by ¥0.09.
Swedish method; Swedish rounding
Cash rounding or Swedish rounding (New Zealand English) occurs when the minimum unit of account is smaller than the lowest physical denomination of currency. The amount payable for a cash transaction is rounded to the nearest multiple of the minimum currency unit available, whereas transactions paid in other ways are not rounded (for example electronic funds transfer like credit cards, or negotiable instruments like cheques).

Wikipedia

Rounding

Rounding means replacing a number with an approximate value that has a shorter, simpler, or more explicit representation. For example, replacing $23.4476 with $23.45, the fraction 312/937 with 1/3, or the expression 2 with 1.414.

Rounding is often done to obtain a value that is easier to report and communicate than the original. Rounding can also be important to avoid misleadingly precise reporting of a computed number, measurement, or estimate; for example, a quantity that was computed as 123,456 but is known to be accurate only to within a few hundred units is usually better stated as "about 123,500".

On the other hand, rounding of exact numbers will introduce some round-off error in the reported result. Rounding is almost unavoidable when reporting 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.

A wavy equals sign (: approximately equal to) is sometimes used to indicate rounding of exact numbers, e.g., 9.98 ≈ 10. This sign was introduced by Alfred George Greenhill in 1892.

Ideal characteristics of rounding methods include:

  1. Rounding should be done by a function. This way, when the same input is rounded in different instances, the output is unchanged.
  2. Calculations done with rounding should be close to those done without rounding.
    • As a result of (1) and (2), the output from rounding should be close to its input, often as close as possible by some metric.
  3. To be considered rounding, the range will be a subset of the domain, in general discrete. A classical range is the integers, Z.
  4. Rounding should preserve symmetries that already exist between the domain and range. With finite precision (or a discrete domain), this translates to removing bias.
  5. A rounding method should have utility in computer science or human arithmetic where finite precision is used, and speed is a consideration.

Because it is not usually possible for a method to satisfy all ideal characteristics, many different rounding methods exist.

As a general rule, rounding is idempotent; i.e., once a number has been rounded, rounding it again will not change its value. Rounding functions are also monotonic; i.e., rounding a larger number gives a larger or equal result than rounding a smaller number. In the general case of a discrete range, they are piecewise constant functions.