Scientific Notation
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Scientific Notation
Scientific notation is a way of expressing numbers that are too large or too small (usually would result in a long string of digits) to be conveniently written in decimal form. It may be referred to as scientific form or standard index form, or standard form in the United Kingdom. This base ten notation is commonly used by scientists, mathematicians, and engineers, in part because it can simplify certain arithmetic operations. On scientific calculators it is usually known as "SCI" display mode. In scientific notation, nonzero numbers are written in the form or ''m'' times ten raised to the power of ''n'', where ''n'' is an integer, and the coefficient ''m'' is a nonzero real number (usually between 1 and 10 in absolute value, and nearly always written as a terminating decimal). The integer ''n'' is called the exponent and the real number ''m'' is called the '' significand'' or ''mantissa''. The term "mantissa" can be ambiguous where logarithms are involved, because it is ...
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Real Numbers
In mathematics, a real number is a number that can be used to measure a ''continuous'' one-dimensional quantity such as a distance, duration or temperature. Here, ''continuous'' means that values can have arbitrarily small variations. Every real number can be almost uniquely represented by an infinite decimal expansion. The real numbers are fundamental in calculus (and more generally in all mathematics), in particular by their role in the classical definitions of limits, continuity and derivatives. The set of real numbers is denoted or \mathbb and is sometimes called "the reals". The adjective ''real'' in this context was introduced in the 17th century by René Descartes to distinguish real numbers, associated with physical reality, from imaginary numbers (such as the square roots of ), which seemed like a theoretical contrivance unrelated to physical reality. The real numbers include the rational numbers, such as the integer and the fraction . The rest of the rea ...
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