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The ratio of the Earth's size to the generating globe's size is called the nominal scale (also called principal scale or representative fraction). Many maps state the nominal scale and may even display a bar scale (sometimes merely called a "scale") to represent it. The second distinct concept of scale applies to the variation in scale across a ...
By mental calculation, it is easier to multiply 16 by 3 ⁄ 16 than to do the same calculation using the fraction's decimal equivalent (0.1875). And it is more precise (exact, in fact) to multiply 15 by 1 ⁄ 3 , for example, than it is to multiply 15 by any decimal approximation of one third.
Later, two classes of such formal definitions emerged, using set theory and Peano's axioms respectively. Later still, they were shown to be equivalent in most practical applications. Set-theoretical definitions of natural numbers were initiated by Frege. He initially defined a natural number as the class of all sets that are in one-to-one ...
Volume percent is the concentration of a certain solute, measured by volume, in a solution.It has as a denominator the volume of the mixture itself, as usual for expressions of concentration, [2] rather than the total of all the individual components’ volumes prior to mixing:
[213] [214] It is considered the mathematical equivalent of the Nobel Prize. [214] Other prestigious mathematics awards include: [215] The Abel Prize, instituted in 2002 [216] and first awarded in 2003 [217] The Chern Medal for lifetime achievement, introduced in 2009 [218] and first awarded in 2010 [219] The AMS Leroy P. Steele Prize, awarded ...
In algebra, the partial fraction decomposition or partial fraction expansion of a rational fraction (that is, a fraction such that the numerator and the denominator are both polynomials) is an operation that consists of expressing the fraction as a sum of a polynomial (possibly zero) and one or several fractions with a simpler denominator. [1]
Addition of fractions is much simpler when the denominators are the same; in this case, one can simply add the numerators while leaving the denominator the same: + = +, so + = + =. [ 63 ] The commutativity and associativity of rational addition is an easy consequence of the laws of integer arithmetic. [ 64 ]
The calculation, conversion, and verification steps took a total of 131 days. [42] In August 2010, Shigeru Kondo used Alexander Yee's y-cruncher to calculate 5 trillion digits of π. This was the world record for any type of calculation, but significantly it was performed on a home computer built by Kondo. [43]