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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.
This is the form of the remainder term mentioned after the actual statement of Taylor's theorem with remainder in the mean value form. The Lagrange form of the remainder is found by choosing G ( t ) = ( x − t ) k + 1 {\displaystyle G(t)=(x-t)^{k+1}} and the Cauchy form by choosing G ( t ) = t − a {\displaystyle G(t)=t-a} .
The molar volume of an ideal gas at 100 kPa (1 bar) is 0.022 710 954 641 485... m 3 /mol at 0 °C, 0.024 789 570 296 023... m 3 /mol at 25 °C. The molar volume of an ideal gas at 1 atmosphere of pressure is 0.022 413 969 545 014... m 3 /mol at 0 °C, 0.024 465 403 697 038... m 3 /mol at 25 °C.
A method analogous to piece-wise linear approximation but using only arithmetic instead of algebraic equations, uses the multiplication tables in reverse: the square root of a number between 1 and 100 is between 1 and 10, so if we know 25 is a perfect square (5 × 5), and 36 is a perfect square (6 × 6), then the square root of a number greater than or equal to 25 but less than 36, begins with ...
RGB values are usually given in the 0–255 range; if they are in the 0–1 range, the values are multiplied by 255 before conversion. This number divided by sixteen (integer division; ignoring any remainder) gives the first hexadecimal digit (between 0 and F, where the letters A to F represent the numbers 10 to 15. See hexadecimal for more ...
Thanks to Hamilton's support, Jefferson receives 30 votes to Burr's 20 and is elected. If all of Hamilton's supporters had instead backed Burr, the election for the last seat would have been exactly tied, requiring a tiebreaker; generally, ties are broken by taking the limit of the results as the quota approaches the exact Droop quota.
On November 20, 1985 (39 years ago) (), the first retail release, Windows 1.01, was released in the United States at a cost of US$99 (equivalent to about $280.00 in 2023). [ 16 ] [ 17 ] In May 1986, the next release, 1.02, was published mainly for the European market, also introducing non-English versions of Windows 1.0.
Statistical subregions as defined by the United Nations Statistics Division [1]. This is the list of countries and other inhabited territories of the world by total population, based on estimates published by the United Nations in the 2024 revision of World Population Prospects.