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Simplification is the process of replacing a mathematical expression by an equivalent one that is simpler (usually shorter), according to a well-founded ordering. Examples include:
Often folded scales start at π but may be extended lengthways to, say, 3.0 and 35.0. Folded scales with the code subscripted with "M" start and finish at log 10 e to simplify conversion between base-10 and natural logarithms.
The Simplified Spelling Board was announced on March 11, 1906, with Andrew Carnegie funding the organization, to be headquartered in New York City. The New York Times noted that Carnegie was convinced that "English might be made the world language of the future" and an influence leading to universal peace, but that this role was obstructed by its "contradictory and difficult spelling". [1]
The Irish logarithm was a system of number manipulation invented by Percy Ludgate for machine multiplication. The system used a combination of mechanical cams as lookup tables and mechanical addition to sum pseudo-logarithmic indices to produce partial products, which were then added to produce results.
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However, 1 and 15 are not within an order of magnitude, since their ratio is 15/1 = 15 > 10. The reciprocal ratio, 1/15, is less than 0.1, so the same result is obtained. Differences in order of magnitude can be measured on a base-10 logarithmic scale in " decades " (i.e., factors of ten). [ 2 ]
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The binomial approximation for the square root, + + /, can be applied for the following expression, + where and are real but .. The mathematical form for the binomial approximation can be recovered by factoring out the large term and recalling that a square root is the same as a power of one half.