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1,3-Butanediol is an organic compound with the formula CH 3 CH (OH)CH 2 CH 2 OH. With two alcohol functional groups, the molecule is classified as a diol. The compound is also chiral, but most studies do not distinguish the enantiomers. The compound is a colorless, bittersweet, water-soluble liquid. It is one of four common structural isomers ...
The 1,3-dipolar cycloaddition is a chemical reaction between a 1,3-dipole and a dipolarophile to form a five-membered ring. The earliest 1,3-dipolar cycloadditions were described in the late 19th century to the early 20th century, following the discovery of 1,3-dipoles. Mechanistic investigation and synthetic application were established in the ...
So this particular repeating decimal corresponds to the fraction 1 / 10 n − 1, where the denominator is the number written as n 9s. Knowing just that, a general repeating decimal can be expressed as a fraction without having to solve an equation. For example, one could reason:
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The graph forms a rectangular hyperbola. In mathematics, a multiplicative inverse or reciprocal for a number x, denoted by 1/ x or x−1, is a number which when multiplied by x yields the multiplicative identity, 1. The multiplicative inverse of a fraction a / b is b / a. For the multiplicative inverse of a real number, divide 1 by the number.
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