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  2. Repeating decimal - Wikipedia

    en.wikipedia.org/wiki/Repeating_decimal

    A repeating decimal or recurring decimal is a decimal representation of a number whose digits are eventually periodic (that is, after some place, the same sequence of digits is repeated forever); if this sequence consists only of zeros (that is if there is only a finite number of nonzero digits), the decimal is said to be terminating, and is not considered as repeating.

  3. Reciprocals of primes - Wikipedia

    en.wikipedia.org/wiki/Reciprocals_of_primes

    In his later years, George Salmon (1819–1904) concerned himself with the repeating periods of these decimal representations of reciprocals of primes. [ 1 ] Contemporaneously, William Shanks (1812–1882) calculated numerous reciprocals of primes and their repeating periods, and published two papers "On Periods in the Reciprocals of Primes" in ...

  4. Midy's theorem - Wikipedia

    en.wikipedia.org/wiki/Midy's_theorem

    In mathematics, Midy's theorem, named after French mathematician E. Midy, [1] is a statement about the decimal expansion of fractions a/p where p is a prime and a/p has a repeating decimal expansion with an even period (sequence A028416 in the OEIS). If the period of the decimal representation of a/p is 2n, so that

  5. Decimal representation - Wikipedia

    en.wikipedia.org/wiki/Decimal_representation

    Also the converse is true: The decimal expansion of a rational number is either finite, or endlessly repeating. Finite decimal representations can also be seen as a special case of infinite repeating decimal representations. For example, 36 ⁄ 25 = 1.44 = 1.4400000...; the endlessly repeated sequence is the one-digit sequence "0".

  6. 0.999... - Wikipedia

    en.wikipedia.org/wiki/0.999...

    The Archimedean property: any point x before the finish line lies between two of the points P n (inclusive).. It is possible to prove the equation 0.999... = 1 using just the mathematical tools of comparison and addition of (finite) decimal numbers, without any reference to more advanced topics such as series and limits.

  7. Repdigit - Wikipedia

    en.wikipedia.org/wiki/Repdigit

    The only positive integers that can be non-Brazilian are 1, 6, the primes, and the squares of the primes, for every other number is the product of two factors x and y with 1 < x < y − 1, and can be written as xx in base y − 1. [14] If a square of a prime p 2 is Brazilian, then prime p must satisfy the Diophantine equation

  8. The 3 Most Overpriced Cities in America, According to Gen Z ...

    www.aol.com/finance/3-most-overpriced-cities...

    Learn More: 5 Cities Where Homes Will Be a Total Steal in 2 Years Find Out: 3 Best Florida Cities To Buy Property in the Next 5 Years, According To Real Estate Agents

  9. 142857 - Wikipedia

    en.wikipedia.org/wiki/142857

    The 142857 number sequence is also found in several decimals in which the denominator has a factor of 7. In the examples below, the numerators are all 1, however there are instances where it does not have to be, such as ⁠ 2 / 7 ⁠ (0. 285714). For example, consider the fractions and equivalent decimal values listed below: ⁠ 1 / 7 ⁠ = 0 ...

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