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Rounding

Index 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 $ with $, or the fraction 312/937 with 1/3, or the expression with. [1]

114 relations: Absolute value, Accuracy and precision, Alfred George Greenhill, Apportionment (politics), Approximation, Array data type, ASTM International, École normale supérieure de Lyon, Binary number, Birkhäuser, C (programming language), Cascading Style Sheets, Cash rounding, Celsius, Churchill Eisenhart, Clay tablet, Communication, Computable number, Condition number, Decimal, Digital signal (signal processing), Discrete time and continuous time, Dither, Document Object Model, Double-precision floating-point format, ECMAScript, EE Times, Equals sign, Error diffusion, Estimation, Expected value, Exponentiation, Extended real number line, False precision, Farey sequence, Fixed-point arithmetic, Floating-point arithmetic, Floor and ceiling functions, Floyd–Steinberg dithering, Fortran, Gal's accurate tables, Gelfond–Schneider theorem, GNU MPFR, Goldbach's conjecture, Halting problem, Human computer, IBM, Idempotence, IEEE 754, IEEE 754 revision, ..., Independence (mathematical logic), Integer, Integer (computer science), Integer overflow, Interface description language, Interval arithmetic, ISO 80000-1, JavaScript, Kahan summation algorithm, Largest remainder method, Library (computing), Lindemann–Weierstrass theorem, Logarithm, Lumber, Machine learning, Measurement, Mesopotamia, Meteorology, Monotonic function, Monte Carlo method, Multiplicative inverse, Multiply–accumulate operation, Nearest integer function, Number, Permutation, PHP, Physical quantity, Pi, Preferred number, Printf format string, Programming language, Propagation of uncertainty, Proportional representation, Pulse-width modulation, Quantization (signal processing), Randomness, Rational number, Report, Robert Simpson Woodward, Round-off error, Scalable Vector Graphics, Share price, Sign function, Signed-digit representation, Significant figures, Sine, Square root, Stern–Brocot tree, Stochastic, Stock market index, Strictfp, Sun Microsystems, Thomas Hare (political scientist), Transcendental function, Transcendental number, Truncation, Two's complement, Unit in the last place, United States, Value-added tax, Vancouver Stock Exchange, Variable (computer science), William Kahan, X87. Expand index (64 more) »

Absolute value

In mathematics, the absolute value or modulus of a real number is the non-negative value of without regard to its sign.

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Accuracy and precision

Precision is a description of random errors, a measure of statistical variability.

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Alfred George Greenhill

Sir (Alfred) George Greenhill, F.R.S. (29 November 1847 in London – 10 February 1927 in London), was a British mathematician.

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Apportionment (politics)

Apportionment is the process by which seats in a legislative body are distributed among administrative divisions entitled to representation.

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Approximation

An approximation is anything that is similar but not exactly equal to something else.

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Array data type

Language support for array types may include certain built-in array data types, some syntactic constructions (array type constructors) that the programmer may use to define such types and declare array variables, and special notation for indexing array elements.

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ASTM International

ASTM International is an international standards organization that develops and publishes voluntary consensus technical standards for a wide range of materials, products, systems, and services.

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École normale supérieure de Lyon

The École normale supérieure de Lyon (also known as ENS Lyon, ENSL or Normale Sup' Lyon) is a highly selective grande école located in Lyon, France.

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Binary number

In mathematics and digital electronics, a binary number is a number expressed in the base-2 numeral system or binary numeral system, which uses only two symbols: typically 0 (zero) and 1 (one).

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Birkhäuser

Birkhäuser is a former Swiss publisher founded in 1879 by Emil Birkhäuser.

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C (programming language)

C (as in the letter ''c'') is a general-purpose, imperative computer programming language, supporting structured programming, lexical variable scope and recursion, while a static type system prevents many unintended operations.

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Cascading Style Sheets

Cascading Style Sheets (CSS) is a style sheet language used for describing the presentation of a document written in a markup language like HTML.

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Cash 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.

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Celsius

The Celsius scale, previously known as the centigrade scale, is a temperature scale used by the International System of Units (SI).

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Churchill Eisenhart

Churchill Eisenhart (1913–1994) was a United States mathematician.

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Clay tablet

In the Ancient Near East, clay tablets (Akkadian ṭuppu(m) 𒁾) were used as a writing medium, especially for writing in cuneiform, throughout the Bronze Age and well into the Iron Age.

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Communication

Communication (from Latin commūnicāre, meaning "to share") is the act of conveying intended meanings from one entity or group to another through the use of mutually understood signs and semiotic rules.

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Computable number

In mathematics, computable numbers are the real numbers that can be computed to within any desired precision by a finite, terminating algorithm.

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Condition number

In the field of numerical analysis, the condition number of a function with respect to an argument measures how much the output value of the function can change for a small change in the input argument.

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Decimal

The decimal numeral system (also called base-ten positional numeral system, and occasionally called denary) is the standard system for denoting integer and non-integer numbers.

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Digital signal (signal processing)

In the context of digital signal processing (DSP), a digital signal is a discrete-time signal for which not only the time but also the amplitude has discrete values; in other words, its samples take on only values from a discrete set (a countable set that can be mapped one-to-one to a subset of integers).

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Discrete time and continuous time

In mathematics and in particular mathematical dynamics, discrete time and continuous time are two alternative frameworks within which to model variables that evolve over time.

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Dither

Dither is an intentionally applied form of noise used to randomize quantization error, preventing large-scale patterns such as color banding in images.

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Document Object Model

The Document Object Model (DOM) is a cross-platform and language-independent application programming interface that treats an HTML, XHTML, or XML document as a tree structure wherein each node is an object representing a part of the document.

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Double-precision floating-point format

Double-precision floating-point format is a computer number format, usually occupying 64 bits in computer memory; it represents a wide dynamic range of numeric values by using a floating radix point.

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ECMAScript

ECMAScript (or ES) is a trademarked scripting-language specification standardized by Ecma International in ECMA-262 and ISO/IEC 16262.

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EE Times

EE Times (Electronic Engineering Times) is an online electronics industry magazine published in the United States by AspenCore Media an Arrow Electronics company.

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Equals sign

The equals sign or equality sign is a mathematical symbol used to indicate equality.

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Error diffusion

Error diffusion is a type of halftoning in which the quantization residual is distributed to neighboring pixels that have not yet been processed.

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Estimation

Estimation (or estimating) is the process of finding an estimate, or approximation, which is a value that is usable for some purpose even if input data may be incomplete, uncertain, or unstable.

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Expected value

In probability theory, the expected value of a random variable, intuitively, is the long-run average value of repetitions of the experiment it represents.

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Exponentiation

Exponentiation is a mathematical operation, written as, involving two numbers, the base and the exponent.

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Extended real number line

In mathematics, the affinely extended real number system is obtained from the real number system by adding two elements: and (read as positive infinity and negative infinity respectively).

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False precision

False precision (also called overprecision, fake precision, misplaced precision and spurious precision) occurs when numerical data are presented in a manner that implies better precision than is justified; since precision is a limit to accuracy, this often leads to overconfidence in the accuracy, named precision bias.

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Farey sequence

In mathematics, the Farey sequence of order n is the sequence of completely reduced fractions between 0 and 1 which when in lowest terms have denominators less than or equal to n, arranged in order of increasing size.

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Fixed-point arithmetic

In computing, a fixed-point number representation is a real data type for a number that has a fixed number of digits after (and sometimes also before) the radix point (after the decimal point '.' in English decimal notation).

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Floating-point arithmetic

In computing, floating-point arithmetic is arithmetic using formulaic representation of real numbers as an approximation so as to support a trade-off between range and precision.

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Floor and ceiling functions

In mathematics and computer science, the floor function is the function that takes as input a real number x and gives as output the greatest integer less than or equal to x, denoted \operatorname(x).

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Floyd–Steinberg dithering

Floyd–Steinberg dithering is an image dithering algorithm first published in 1976 by Robert W. Floyd and Louis Steinberg.

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Fortran

Fortran (formerly FORTRAN, derived from Formula Translation) is a general-purpose, compiled imperative programming language that is especially suited to numeric computation and scientific computing.

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Gal's accurate tables

Gal's accurate tables is a method devised by Shmuel Gal to provide accurate values of special functions using a lookup table and interpolation.

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Gelfond–Schneider theorem

In mathematics, the Gelfond–Schneider theorem establishes the transcendence of a large class of numbers.

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GNU MPFR

GNU MPFR (GNU Multiple Precision Floating-Point Reliably) is a GNU portable C library for arbitrary-precision binary floating-point computation with correct rounding, based on GNU Multi-Precision Library.

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Goldbach's conjecture

Goldbach's conjecture is one of the oldest and best-known unsolved problems in number theory and all of mathematics.

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Halting problem

In computability theory, the halting problem is the problem of determining, from a description of an arbitrary computer program and an input, whether the program will finish running (i.e., halt) or continue to run forever.

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Human computer

The term "computer", in use from the early 17th century (the first known written reference dates from 1613), meant "one who computes": a person performing mathematical calculations, before electronic computers became commercially available.

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IBM

The International Business Machines Corporation (IBM) is an American multinational technology company headquartered in Armonk, New York, United States, with operations in over 170 countries.

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Idempotence

Idempotence is the property of certain operations in mathematics and computer science that they can be applied multiple times without changing the result beyond the initial application.

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IEEE 754

The IEEE Standard for Floating-Point Arithmetic (IEEE 754) is a technical standard for floating-point computation established in 1985 by the Institute of Electrical and Electronics Engineers (IEEE).

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IEEE 754 revision

IEEE 754-2008 (previously known as IEEE 754r) was published in August 2008 and is a significant revision to, and replaces, the IEEE 754-1985 floating point standard.

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Independence (mathematical logic)

In mathematical logic, independence refers to the unprovability of a sentence from other sentences.

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Integer

An integer (from the Latin ''integer'' meaning "whole")Integer 's first literal meaning in Latin is "untouched", from in ("not") plus tangere ("to touch").

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Integer (computer science)

In computer science, an integer is a datum of integral data type, a data type that represents some range of mathematical integers.

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Integer overflow

In computer programming, an integer overflow occurs when an arithmetic operation attempts to create a numeric value that is outside of the range that can be represented with a given number of bits – either larger than the maximum or lower than the minimum representable value.

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Interface description language

An interface description language or interface definition language (IDL), is a specification language used to describe a software component's application programming interface (API).

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Interval arithmetic

Interval arithmetic, interval mathematics, interval analysis, or interval computation, is a method developed by mathematicians since the 1950s and 1960s, as an approach to putting bounds on rounding errors and measurement errors in mathematical computation and thus developing numerical methods that yield reliable results.

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ISO 80000-1

ISO 80000-1:2009 is a standard describing scientific and mathematical quantities and their units.

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JavaScript

JavaScript, often abbreviated as JS, is a high-level, interpreted programming language.

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Kahan summation algorithm

In numerical analysis, the Kahan summation algorithm (also known as compensated summation) significantly reduces the numerical error in the total obtained by adding a sequence of finite precision floating point numbers, compared to the obvious approach.

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Largest remainder method

The largest remainder method (also known as Hare-Niemeyer method, Hamilton method or as Vinton's method) is one way of allocating seats proportionally for representative assemblies with party list voting systems.

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Library (computing)

In computer science, a library is a collection of non-volatile resources used by computer programs, often for software development.

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Lindemann–Weierstrass theorem

In transcendental number theory, the Lindemann–Weierstrass theorem is a result that is very useful in establishing the transcendence of numbers.

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Logarithm

In mathematics, the logarithm is the inverse function to exponentiation.

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Lumber

Lumber (American English; used only in North America) or timber (used in the rest of the English speaking world) is a type of wood that has been processed into beams and planks, a stage in the process of wood production.

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Machine learning

Machine learning is a subset of artificial intelligence in the field of computer science that often uses statistical techniques to give computers the ability to "learn" (i.e., progressively improve performance on a specific task) with data, without being explicitly programmed.

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Measurement

Measurement is the assignment of a number to a characteristic of an object or event, which can be compared with other objects or events.

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Mesopotamia

Mesopotamia is a historical region in West Asia situated within the Tigris–Euphrates river system, in modern days roughly corresponding to most of Iraq, Kuwait, parts of Northern Saudi Arabia, the eastern parts of Syria, Southeastern Turkey, and regions along the Turkish–Syrian and Iran–Iraq borders.

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Meteorology

Meteorology is a branch of the atmospheric sciences which includes atmospheric chemistry and atmospheric physics, with a major focus on weather forecasting.

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Monotonic function

In mathematics, a monotonic function (or monotone function) is a function between ordered sets that preserves or reverses the given order.

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Monte Carlo method

Monte Carlo methods (or Monte Carlo experiments) are a broad class of computational algorithms that rely on repeated random sampling to obtain numerical results.

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Multiplicative inverse

In mathematics, a multiplicative inverse or reciprocal for a number x, denoted by 1/x or x−1, is a number which when multiplied by x yields the multiplicative identity, 1.

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Multiply–accumulate operation

In computing, especially digital signal processing, the multiply–accumulate operation is a common step that computes the product of two numbers and adds that product to an accumulator.

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Nearest integer function

In computer science, the nearest integer function of real number x denoted variously by, \lfloor x \rceil, \Vert x \Vert, nint(x), or Round(x), is a function which returns the nearest integer to x. To avoid ambiguity when operating on half-integers, a rounding rule must be chosen.

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Number

A number is a mathematical object used to count, measure and also label.

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Permutation

In mathematics, the notion of permutation relates to the act of arranging all the members of a set into some sequence or order, or if the set is already ordered, rearranging (reordering) its elements, a process called permuting.

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PHP

PHP: Hypertext Preprocessor (or simply PHP) is a server-side scripting language designed for Web development, but also used as a general-purpose programming language.

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Physical quantity

A physical quantity is a physical property of a phenomenon, body, or substance, that can be quantified by measurement.or we can say that quantities which we come across during our scientific studies are called as the physical quantities...

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Pi

The number is a mathematical constant.

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Preferred number

In industrial design, preferred numbers (also called preferred values or preferred series) are standard guidelines for choosing exact product dimensions within a given set of constraints.

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Printf format string

Printf format string refers to a control parameter used by a class of functions in the input/output libraries of C and many other programming languages.

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Programming language

A programming language is a formal language that specifies a set of instructions that can be used to produce various kinds of output.

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Propagation of uncertainty

In statistics, propagation of uncertainty (or propagation of error) is the effect of variables' uncertainties (or errors, more specifically random errors) on the uncertainty of a function based on them.

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Proportional representation

Proportional representation (PR) characterizes electoral systems by which divisions into an electorate are reflected proportionately into the elected body.

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Pulse-width modulation

Pulse-width modulation (PWM), or pulse-duration modulation (PDM), is a modulation technique used to encode a message into a pulsing signal.

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Quantization (signal processing)

Quantization, in mathematics and digital signal processing, is the process of mapping input values from a large set (often a continuous set) to output values in a (countable) smaller set.

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Randomness

Randomness is the lack of pattern or predictability in events.

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Rational number

In mathematics, a rational number is any number that can be expressed as the quotient or fraction of two integers, a numerator and a non-zero denominator.

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Report

A report or account is an informational work, such as writing, speech, television or film, made with the intention of relaying information or recounting events in a presentable form.

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Robert Simpson Woodward

Robert Simpson Woodward (July 21, 1849 – June 29, 1924) was an American civil engineer, physicist and mathematician.

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Round-off error

A round-off error, also called rounding error, is the difference between the calculated approximation of a number and its exact mathematical value due to rounding.

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Scalable Vector Graphics

Scalable Vector Graphics (SVG) is an XML-based vector image format for two-dimensional graphics with support for interactivity and animation.

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Share price

A share price is the price of a single share of a number of saleable stocks of a company, derivative or other financial asset.

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Sign function

In mathematics, the sign function or signum function (from signum, Latin for "sign") is an odd mathematical function that extracts the sign of a real number.

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Signed-digit representation

In mathematical notation for numbers, signed-digit representation is a positional system with signed digits; the representation may not be unique.

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Significant figures

The significant figures (also known as the significant digits) of a number are digits that carry meaning contributing to its measurement resolution.

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Sine

In mathematics, the sine is a trigonometric function of an angle.

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Square root

In mathematics, a square root of a number a is a number y such that; in other words, a number y whose square (the result of multiplying the number by itself, or) is a. For example, 4 and −4 are square roots of 16 because.

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Stern–Brocot tree

In number theory, the Stern–Brocot tree is an infinite complete binary tree in which the vertices correspond one-for-one to the positive rational numbers, whose values are ordered from the left to the right as in a search tree.

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Stochastic

The word stochastic is an adjective in English that describes something that was randomly determined.

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Stock market index

A stock index or stock market index is a measurement of a section of the stock market.

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Strictfp

strictfp is a keyword in the Java programming language that restricts floating-point calculations to ensure portability.

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Sun Microsystems

Sun Microsystems, Inc. was an American company that sold computers, computer components, software, and information technology services and created the Java programming language, the Solaris operating system, ZFS, the Network File System (NFS), and SPARC.

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Thomas Hare (political scientist)

Sir Thomas Hare (28 March 1806 in England – 6 May 1891) was a British proponent of electoral reform.

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Transcendental function

A transcendental function is an analytic function that does not satisfy a polynomial equation, in contrast to an algebraic function.

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Transcendental number

In mathematics, a transcendental number is a real or complex number that is not algebraic—that is, it is not a root of a nonzero polynomial equation with integer (or, equivalently, rational) coefficients.

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Truncation

In mathematics and computer science, truncation is limiting the number of digits right of the decimal point.

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Two's complement

Two's complement is a mathematical operation on binary numbers, best known for its role in computing as a method of signed number representation.

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Unit in the last place

In computer science and numerical analysis, unit in the last place or unit of least precision (ULP) is the spacing between floating-point numbers, i.e., the value the least significant digit represents if it is 1.

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United States

The United States of America (USA), commonly known as the United States (U.S.) or America, is a federal republic composed of 50 states, a federal district, five major self-governing territories, and various possessions.

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Value-added tax

A value-added tax (VAT), known in some countries as a goods and services tax (GST), is a type of tax that is assessed incrementally, based on the increase in value of a product or service at each stage of production or distribution.

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Vancouver Stock Exchange

The Vancouver Stock Exchange (VSE) was a stock exchange based in Vancouver, British Columbia.

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Variable (computer science)

In computer programming, a variable or scalar is a storage location (identified by a memory address) paired with an associated symbolic name (an identifier), which contains some known or unknown quantity of information referred to as a value.

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William Kahan

William "Velvel" Morton Kahan (born June 5, 1933) is a Canadian mathematician and computer scientist who received the Turing Award in 1989 for "his fundamental contributions to numerical analysis", was named an ACM Fellow in 1994, and inducted into the National Academy of Engineering in 2005.

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X87

x87 is a floating point-related subset of the x86 architecture instruction set.

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Redirects here:

ASTM rounding, Banker's rounding, Bankers rounding, Bankers' rounding, Directed rounding, Dutch rounding, Gaussian rounding, Round to even, Round to odd, Round-to-odd, Rounding function, Rounding functions, Rounding numbers, Rounding to integer, Rounding to odd, Rounding-to-odd, Statistician's rounding, Sticky round, Sticky rounding, Sticky-round, Stochastic rounding, Table-maker's dilemma, Unbiased rounding.

References

[1] https://en.wikipedia.org/wiki/Rounding

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