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  2. Fraction - Wikipedia

    en.wikipedia.org/wiki/Fraction

    The reciprocal of ⁠ 3 / 7 ⁠, for instance, is ⁠ 7 / 3 ⁠. The product of a 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 ...

  3. Pi - Wikipedia

    en.wikipedia.org/wiki/Pi

    Truncating the continued fraction at any point yields a rational approximation for π; the first four of these are 3, ⁠ 22 / 7 ⁠, ⁠ 333 / 106 ⁠, and ⁠ 355 / 113 ⁠. These numbers are among the best-known and most widely used historical approximations of the constant.

  4. Egyptian fraction - Wikipedia

    en.wikipedia.org/wiki/Egyptian_fraction

    An Egyptian fraction is a finite sum of distinct unit fractions, such as That is, each fraction in the expression has a numerator equal to 1 and a denominator that is a positive integer, and all the denominators differ from each other. The value of an expression of this type is a positive rational number ; for instance the Egyptian fraction ...

  5. Repeating decimal - Wikipedia

    en.wikipedia.org/wiki/Repeating_decimal

    For example, the fraction ⁠ 2 / 7 ⁠ has d = 7, and the smallest k that makes 10 k − 1 divisible by 7 is k = 6, because 999999 = 7 × 142857. The period of the fraction ⁠ 2 / 7 ⁠ is therefore 6.

  6. Continued fraction - Wikipedia

    en.wikipedia.org/wiki/Continued_fraction

    Continued fraction. A finite regular continued fraction, where is a non-negative integer, is an integer, and is a positive integer, for . In mathematics, a continued fraction is an expression obtained through an iterative process of representing a number as the sum of its integer part and the reciprocal of another number, then writing this ...

  7. Proof that 22/7 exceeds π - Wikipedia

    en.wikipedia.org/wiki/Proof_that_22/7_exceeds_π

    22 7 ⁠ is a widely used Diophantine approximation of π. It is a convergent in the simple continued fraction expansion of π. It is greater than π, as can be readily seen in the decimal expansions of these values: The approximation has been known since antiquity. Archimedes wrote the first known proof that ⁠ 22 7 ⁠ is an overestimate in ...

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