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The following list includes a decimal expansion and set containing ... 4, 1, 1, 6, 1, 1, 8, 1, 1, 10, 1, 1 ... Then √γ n n is the maximum of λ 1 (L) over all such ...
In mathematics, the Leibniz formula for π, named after Gottfried Wilhelm Leibniz, states that = + + = = +,. an alternating series.. It is sometimes called the Madhava–Leibniz series as it was first discovered by the Indian mathematician Madhava of Sangamagrama or his followers in the 14th–15th century (see Madhava series), [1] and was later independently rediscovered by James Gregory in ...
To change 1 / 3 to a decimal, divide 1.000... by 3 (" 3 into 1.000... "), and stop when the desired accuracy is obtained, e.g., at 4 decimals with 0.3333. The fraction 1 / 4 can be written exactly with two decimal digits, while the fraction 1 / 3 cannot be written exactly as a
If the sides of a rectangle are measured as 1.23 m and 4.56 m, then multiplication gives an area for the rectangle between 5.614591 m 2 and 5.603011 m 2. Since not even the second digit after the decimal place is preserved, the following digits are not significant. Therefore, the result is usually rounded to 5.61.
Plouffe's series for calculating arbitrary decimal digits of ... Number Theory 1: Fermat's Dream. American Mathematical Society, Providence 1993, ...
The magnitude of such precision (152 decimal places) can be put into context by the fact that the circumference of the largest known object, the observable universe, can be calculated from its diameter (93 billion light-years) to a precision of less than one Planck length (at 1.6162 × 10 −35 meters, the shortest unit of length expected to be ...
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The set of rational numbers is not complete. For example, the sequence (1; 1.4; 1.41; 1.414; 1.4142; 1.41421; ...), where each term adds a digit of the decimal expansion of the positive square root of 2, is Cauchy but it does not converge to a rational number (in the real numbers, in contrast, it converges to the positive square root of 2).