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Zero to the power of zero, denoted as 0 0, is a mathematical expression that can take different values depending on the context. In certain areas of mathematics, such as combinatorics and algebra, 0 0 is conventionally defined as 1 because this assignment simplifies many formulas and ensures consistency in operations involving exponents.
For example, in base 2 (the binary numeral system) 0.111... equals 1, and in base 3 (the ternary numeral system) 0.222... equals 1. In general, any terminating base expression has a counterpart with repeated trailing digits equal to − 1. Textbooks of real analysis are likely to skip the example of 0.999... and present one or both of these ...
Units of activity (the curie and the becquerel) also refer to a quantity of radioactive atoms. Because the probability of decay is a fixed physical quantity, for a known number of atoms of a particular radionuclide, a predictable number will decay in a given time.
For example, the quotient can be defined to equal zero; it can be defined to equal a new explicit point at infinity, sometimes denoted by the infinity symbol; or it can be defined to result in signed infinity, with positive or negative sign depending on the sign of the dividend. In these number systems division by zero is no longer a special ...
Molar concentration or molarity is most commonly expressed in units of moles of solute per litre of solution. [2] For use in broader applications, it is defined as amount of substance of solute per unit volume of solution, or per unit volume available to the species, represented by lowercase : [3]
The decibel (symbol: dB) is a relative unit of measurement equal to one tenth of a bel (B). It expresses the ratio of two values of a power or root-power quantity on a logarithmic scale . Two signals whose levels differ by one decibel have a power ratio of 10 1/10 (approximately 1.26 ) or root-power ratio of 10 1/20 (approximately 1.12 ).
A googol is the large number 10 100 or ten to the power of one hundred. In decimal notation, it is written as the digit 1 followed by one hundred zeroes: 10, 000, 000 ...
A related concept is one part per ten thousand, 1 / 10,000 .The same unit is also (rarely) called a permyriad, literally meaning "for (every) myriad (ten thousand)". [4] [5] If used interchangeably with basis point, the permyriad is potentially confusing because an increase of one basis point to a 10 basis point value is generally understood to mean an increase to 11 basis points; not ...