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v. t. e. The table below is a brief chronology of computed numerical values of, or bounds on, the mathematical constant pi (π). For more detailed explanations for some of these calculations, see Approximations of π. As of July 2024, π has been calculated to 202,112,290,000,000 (approximately 202 trillion) decimal digits.
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 ...
The best-known approximations to π dating before the Common Era were accurate to two decimal places; this was improved upon in Chinese mathematics in particular by the mid-first millennium, to an accuracy of seven decimal places. After this, no further progress was made until the late medieval period.
v. t. e. Piphilology comprises the creation and use of mnemonic techniques to remember many digits of the mathematical constant π. The word is a play on the word "pi" itself and of the linguistic field of philology. There are many ways to memorize π, including the use of piems (a portmanteau, formed by combining pi and po em), which are poems ...
1789 — Jurij Vega improves Machin's formula and computes π to 140 decimal places. 1949 — John von Neumann computes π to 2,037 decimal places using ENIAC. 1961 — Daniel Shanks and John Wrench compute π to 100,000 decimal places using an inverse-tangent identity and an IBM-7090 computer. 1987 — Yasumasa Kanada, David Bailey, Jonathan ...
For example, 6.849999999999... = 6.85 and 6.850000000000... = 6.85. Finally, if all of the digits in a numeral are 0, the number is 0, and if all of the digits in a numeral are an unending string of 9s, you can drop the nines to the right of the decimal place, and add one to the string of 9s to the left of the decimal place.
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v. t. e. Positional notation, also known as place-value notation, positional numeral system, or simply place value, usually denotes the extension to any base of the Hindu–Arabic numeral system (or decimal system). More generally, a positional system is a numeral system in which the contribution of a digit to the value of a number is the value ...