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  2. Reciprocals of primes - Wikipedia

    en.wikipedia.org/wiki/Reciprocals_of_primes

    Rules for calculating the periods of repeating decimals from rational fractions were given by James Whitbread Lee Glaisher in 1878. [5] For a prime p, the period of its reciprocal divides p − 1. [6] The sequence of recurrence periods of the reciprocal primes (sequence A002371 in the OEIS) appears in the 1973 Handbook of Integer Sequences.

  3. 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.

  4. William Shanks - Wikipedia

    en.wikipedia.org/wiki/William_Shanks

    In addition to calculating π, Shanks also calculated e and the Euler–Mascheroni constant γ to many decimal places. He published a table of primes (and the periods of their reciprocals) up to 110,000 and found the natural logarithms of 2, 3, 5 and 10 to 137 places. During his calculations, which took many tedious days of work, Shanks was ...

  5. Division algorithm - Wikipedia

    en.wikipedia.org/wiki/Division_algorithm

    Long division is the standard algorithm used for pen-and-paper division of multi-digit numbers expressed in decimal notation. It shifts gradually from the left to the right end of the dividend, subtracting the largest possible multiple of the divisor (at the digit level) at each stage; the multiples then become the digits of the quotient, and the final difference is then the remainder.

  6. Harmonic number - Wikipedia

    en.wikipedia.org/wiki/Harmonic_number

    The harmonic number with = ⌊ ⌋ (red line) with its asymptotic limit + ⁡ (blue line) where is the Euler–Mascheroni constant.. In mathematics, the n-th harmonic number is the sum of the reciprocals of the first n natural numbers: [1] = + + + + = =.

  7. Fraction - Wikipedia

    en.wikipedia.org/wiki/Fraction

    The product of a non-zero fraction and its reciprocal is 1, hence the reciprocal is the multiplicative inverse of a fraction. The reciprocal of a proper fraction is improper, and the reciprocal of an improper fraction not equal to 1 (that is, numerator and denominator are not equal) is a proper fraction.

  8. FDA approves new type of non-opioid pain medication, 1st of ...

    www.aol.com/news/fda-approves-type-non-opioid...

    The U.S. Food and Drug Administration (FDA) on Thursday approved a new type of prescription pain medication for adults to treat moderate to severe acute pain. The drug, called Journavx ...

  9. List of sums of reciprocals - Wikipedia

    en.wikipedia.org/wiki/List_of_sums_of_reciprocals

    The sum of the reciprocals of the powerful numbers is close to 1.9436 . [4] The reciprocals of the factorials sum to the transcendental number e (one of two constants called "Euler's number"). The sum of the reciprocals of the square numbers (the Basel problem) is the transcendental number ⁠ π 2 / 6 ⁠, or ζ(2) where ζ is the Riemann zeta ...

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