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Significant Figures
The significant figures of a number are digits that carry meaning contributing to its measurement resolution. This includes all digits except:[1]All leading zeros; Trailing zeros when they are merely placeholders to indicate the scale of the number (exact rules are explained at identifying significant figures); and Spurious digits introduced, for example, by calculations carried out to greater precision than that of the original data, or measurements reported to a greater precision than the equipment supports. Significance arithmetic are approximate rules for roughly maintaining significance throughout a computation
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Round-off Error
A round-off error,[1] also called rounding error,[2] is the difference between the calculated approximation of a number and its exact mathematical value due to rounding. This is a form of quantization error.[3] One of the goals of numerical analysis is to estimate errors in calculations, including round-off error, when using approximation equations or algorithms, especially when using finitely many digits to represent real numbers (which in theory have infinitely many digits).[4] When a sequence of calculations subject to rounding error is made, errors may accumulate, sometimes dominating the calculation
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Normalized Number
In applied mathematics, a number is normalized when it is written in scientific notation with one nonzero decimal digit before the decimal point.[1] Thus, a real number when written out in normalized scientific notation is as follows: ± d 0 . d 1 d 2 d 3 ⋯ × 10 n displaystyle pm d_ 0 .d_ 1 d_ 2 d_ 3 dots times 10^ n where n is an integer, d 0 , displaystyle d_ 0 , d 1 , displaystyle d_ 1 , d 2 displaystyle d_ 2 , d 3 displaystyle d_ 3 ... are the digits of the number in base 10, and d 0 displaystyle d_ 0 is not zero. That is, its leading digit (i.e. leftmost) is not zero and is followed by the decimal point
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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 displaystyle x and gives as output the greatest integer less than or equal to x displaystyle x , denoted floor ( x ) = ⌊ x ⌋ displaystyle text floor (x)=lfloor xrfloor
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Absolute Value
In mathematics, the absolute value or modulus x of a real number x is the non-negative value of x without regard to its sign. Namely, x = x for a positive x, x = −x for a negative x (in which case −x is positive), and 0 = 0. For example, the absolute value of 3 is 3, and the absolute value of −3 is also 3. The absolute value of a number may be thought of as its distance from zero. Generalisations of the absolute value for real numbers occur in a wide variety of mathematical settings. For example, an absolute value is also defined for the complex numbers, the quaternions, ordered rings, fields and vector spaces
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Area Of A Disk
In geometry, the area enclosed by a circle of radius r is π r2. Here the Greek letter π represents a constant, approximately equal to 3.14159, which is equal to the ratio of the circumference of any circle to its diameter. One method of deriving this formula, which originated with Archimedes, involves viewing the circle as the limit of a sequence of regular polygons. The area of a regular polygon is half its perimeter multiplied by the distance from its center to its sides, and the corresponding formula (that the area is half the perimeter times the radius, i.e. ​1⁄2 × 2πr × r) holds in the limit for a circle. Although often referred to as the area of a circle in informal contexts, strictly speaking the term disk refers to the interior of the circle, while circle is reserved for the boundary only, which is a curve and covers no area itself
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Kinetic Energy
Ek = ½mv2 Ek = Et+ErPart of a series of articles aboutClassical mechanics F → = m a → displaystyle vec F =m vec a Second law of motionHistory TimelineBranchesApplied Celestial Continuum Dynamics Kinematics Kinetics Statics StatisticalFundamentalsAcceleration Angular momentum Couple D'Alembert's principle Energykinetic potentialForce Frame of reference Inertial frame of reference Impulse Inertia / Moment of inertia MassMechanical power Mechanical workMoment Momentum Space Speed Time Torque Velocity Virtual workFormulationsNewton's laws of motionAnalytical mechanicsLagrangian mechanics Hamiltonian mechanics Routhian mechanics Hamilton–Jacobi equation Appell's equation of motion Udwadia–Kalaba equation Koopman–von Neumann mechanicsCore topic
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Positional Notation
Positional notation
Positional notation
or place-value notation is a method of representing or encoding numbers. Positional notation
Positional notation
is distinguished from other notations (such as Roman numerals) for its use of the same symbol for the different orders of magnitude (for example, the "ones place", "tens place", "hundreds place"). This greatly simplified arithmetic, leading to the rapid spread of the notation across the world. With the use of a radix point (decimal point in base-10), the notation can be extended to include fractions and the numeric expansions of real numbers. The Babylonian numeral system, base-60, was the first positional system developed, and its influence is present today in the way time and angles are counted in tallies related to 60, like 60 minutes in an hour, 360 degrees in a circle. The Hindu–Arabic numeral system, base-10, is the most commonly used system in the world today for most calculations
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Base (exponentiation)
In exponentiation, the base is the number b in an expression of the form bn.Contents1 Related terms 2 Roots 3 Logarithms 4 ReferencesRelated terms[edit] The number n is called the exponent and the expression is known formally as exponentiation of b by n or the exponential of n with base b. It is more commonly expressed as "the nth power of b", "b to the nth power" or "b to the power n". For example, the fourth power of 10 is 10,000 because 104 = 10 × 10 × 10 × 10 = 10,000. The term power strictly refers to the entire expression, but is sometimes used to refer to the exponent. Radix
Radix
is the traditional term for base, but usually refers then to one of the common bases: decimal (10), binary (2), hexadecimal (16), or sexagesimal (60)
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Logarithm
In mathematics, the logarithm is the inverse operation to exponentiation, just as division is the inverse of multiplication. That means the logarithm of a number is the exponent to which another fixed number, the base, must be raised to produce that number. In the most simple case the logarithm counts repeated multiplication of the same factor; e.g., since 1000 = 10 × 10 × 10 = 103, the "logarithm to base 10" of 1000 is 3. More generally, exponentiation allows any positive real number to be raised to any real power, always producing a positive result, so the logarithm can be calculated for any two positive real numbers b and x where b is not equal to 1. The logarithm of x to base b, denoted logb (x) (or logb x when no confusion is possible), is the unique real number y such that by = x. For example, log2 64 = 6, as 64 = 26. The logarithm to base 10 (that is b = 10) is called the common logarithm and has many applications in science and engineering
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Common Logarithm
In mathematics, the common logarithm is the logarithm with base 10.[1] It is also known as the decadic logarithm and also as the decimal logarithm, named after its base, or Briggsian logarithm, after Henry Briggs, an English mathematician who pioneered its use, as well as "standard logarithm". Historically, it was known as logarithmus decimalis[2] or logarithmus decadis.[3] It is indicated by log10(x), or sometimes Log(x) with a capital L (however, this notation is ambiguous since it can also mean the complex natural logarithmic multi-valued function). On calculators it is usually "log", but mathematicians usually mean natural logarithm (logarithm with base e ≈ 2.71828) rather than common logarithm when they write "log"
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Plus-minus Sign
The plus-minus sign (±) is a mathematical symbol with multiple meanings.In mathematics, it generally indicates a choice of exactly two possible values, one of which is the negation of the other. In experimental sciences, the sign commonly indicates the confidence interval or error in a measurement, often the standard deviation or standard error.[1] The sign may also represent an inclusive range of values that a reading might have. In engineering the sign indicates the tolerance, which is the range of values that are considered to be acceptable, safe, or which comply with some standard, or with a contract.[2] In botany it is used in morphological descriptions to notate "more or less". In chemistry the sign is used to indicate a racemic mixture. In chess, the sign indicates a clear advantage for the white player; the complementary sign ∓ indicates the same advantage for the black player.[3]The sign is normally pronounced "plus or minus".Contents1 History 2
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Estimation
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. The value is nonetheless usable because it is derived from the best information available.[1] Typically, estimation involves "using the value of a statistic derived from a sample to estimate the value of a corresponding population parameter".[2] The sample provides information that can be projected, through various formal or informal processes, to determine a range most likely to describe the missing information
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Order Of Magnitude
An order of magnitude is an approximate measure of the size of a number, equal to the logarithm (base 10) rounded to a whole number. For example, the order of magnitude of 1500 is 3, because 1500 = 1.5 × 103.The scale of everything
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Binomial Proportion Confidence Interval
In statistics, a binomial proportion confidence interval is a confidence interval for the probability of success calculated from the outcome of a series of success–failure experiments (Bernoulli trials). In other words, a binomial proportion confidence interval is an interval estimate of a success probability p when only the number of experiments n and the number of successes nS are known. There are several formulas for a binomial confidence interval, but all of them rely on the assumption of a binomial distribution. In general, a binomial distribution applies when an experiment is repeated a fixed number of times, each trial of the experiment has two possible outcomes (success and failure), the probability of success is the same for each trial, and the trials are statistically independent
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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). The base-2 numeral system is a positional notation with a radix of 2. Each digit is referred to as a bit
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