1482:. The predictions of a scientific theory can differ from actual measurements. This can be because there are factors in the real situation that are not included in the theory. For example, simple calculations may not include the effect of air resistance. Under these circumstances, the theory is an approximation to reality. Differences may also arise because of limitations in the measuring technique. In this case, the measurement is an approximation to the actual value.
50:
1525:. In the first iteration, the planets' gravitational interactions are ignored, and the star is assumed to be fixed. If a more precise solution is desired, another iteration is then performed, using the positions and motions of the planets as identified in the first iteration, but adding a first-order gravity interaction from each planet on the others. This process may be repeated until a satisfactorily precise solution is obtained.
1940:
322:, slide rules and calculators produce approximate answers to all but the simplest calculations. The results of computer calculations are normally an approximation expressed in a limited number of significant digits, although they can be programmed to produce more precise results. Approximation can occur when a decimal number cannot be expressed in a finite number of binary digits.
300:
being measured is 1,500,000 to the nearest hundred thousand (so the actual value is somewhere between 1,450,000 and 1,550,000); this is in contrast to the notation 1.500 × 10, which means that the true value is 1,500,000 to the nearest thousand (implying that the true value is somewhere between 1,499,500 and 1,500,500).
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Some problems in physics are too complex to solve by direct analysis, or progress could be limited by available analytical tools. Thus, even when the exact representation is known, an approximation may yield a sufficiently accurate solution while reducing the complexity of the problem significantly.
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Approximation usually occurs when an exact form or an exact numerical number is unknown or difficult to obtain. However some known form may exist and may be able to represent the real form so that no significant deviation can be found. For example, 1.5 × 10 means that the true value of something
1520:
Approximation is also used to analyze the motion of several planets orbiting a star. This is extremely difficult due to the complex interactions of the planets' gravitational effects on each other. An approximate solution is effected by performing
253:
In science, approximation can refer to using a simpler process or model when the correct model is difficult to use. An approximate model is used to make calculations easier. Approximations might also be used if incomplete
230:
The term can be applied to various properties (e.g., value, quantity, image, description) that are nearly, but not exactly correct; similar, but not exactly the same (e.g., the approximate time was 10 o'clock).
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is a key word generally employed within the title of a directive, for example the Trade Marks
Directive of 16 December 2015 serves "to approximate the laws of the Member States relating to trade marks". The
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420:. No consistent notation is used throughout mathematics and some texts use ≈ to mean approximately equal and ~ to mean asymptotically equal whereas other texts use the symbols the other way around.
1497:, a new scientific theory should reproduce the results of older, well-established, theories in those domains where the old theories work. The old theory becomes an approximation to the new theory.
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Directive (EU) 2015/2436 of the
European Parliament and of the Council of 16 December 2015 to approximate the laws of the Member States relating to trade marks (recast) (Text with EEA relevance)
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value of a function, i.e. the value as one or more of a function's parameters becomes arbitrarily large. For example, the sum
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European Union".
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Another combination of "≈" and "=", used to indicate equivalence or approximate equivalence.
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are used especially in technical or scientific contexts. In everyday
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Guide to the
Approximation of European Union Environmental Legislation
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are used with a similar meaning. It is often found abbreviated as
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Which can be used to represent the approach of a variable,
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is anything that is intentionally similar but not exactly
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Which is also sometimes used to indicate proportionality.
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A combination of "≈" and "=", which is used to indicate
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is a branch of mathematics, and a quantitative part of
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The type of approximation used depends on the available
1925:, published 23 December 2015, accessed 15 November 2022
1912:, last updated 2 August 2019, accessed 15 November 2022
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would be wrong under this definition, despite wide use.
37:"Approximate" redirects here. Not to be confused with
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1333:{\displaystyle \lim _{x\to \infty }y(x)\doteq 0}
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234:Although approximation is most often applied to
1796:"Approximately Equal — from Wolfram MathWorld"
1665: – Expressions for approximation accuracy
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981:{\displaystyle \Delta ABC\cong \Delta A'B'C'}
325:Related to approximation of functions is the
1844:D & D Standard Oil & Gas Abbreviator
1750:Longman Dictionary of Contemporary English,
1605: – Varying methods used to calculate pi
1489:shows that earlier theories and laws can be
27:Something roughly the same as something else
1695: – Type of analog-to-digital converter
1671: – Approximation of a mathematical set
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1204:NEITHER APPROXIMATELY NOR ACTUALLY EQUAL TO
407:{\displaystyle k/2+k/4+k/8+\cdots +k/2^{n}}
1647: – Approximation method in statistics
583:, was introduced by British mathematician
1099:Which is also sometimes used to indicate
134:Learn how and when to remove this message
1617: – Equivalence relation in algebra
1186:APPROXIMATELY BUT NOT ACTUALLY EQUAL TO
258:prevents use of exact representations.
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697:{\displaystyle 1\not \approx 2}
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548:EQUALS SIGN
508:MINUS TILDE
424:Typography
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1828:2013-04-20
1805:2021-11-22
1781:2013-06-16
1719:References
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1503:Physicists
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