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For Rutherford's alpha particle scattering from gold, with mass of 197, the reduced mass is very close to the mass of the alpha particle: = + = For lighter aluminium, with mass 27, the effect is greater: = + = a 13% difference in mass. Rutherford notes this difference and suggests experiments be performed with lighter atoms.
The law of conservation of mass or principle of mass conservation states that for any system closed to all transfers of matter and energy, the mass of the system must remain constant over time, as system's mass cannot change, so quantity cannot be added nor removed. Hence, the quantity of mass is conserved over time.
Quaoar has a mass of 1.2 × 10 21 kg, which was determined from Weywot's orbit using Kepler's third law. [13] Measurements of Quaoar's diameter and mass as of 2024 [update] indicate it has a density between 1.66–1.77 g/cm 3 , which suggests its interior is composed of roughly 70% rock and 30% ice with low porosity .
The repeating decimal commonly written as 0.999... represents exactly the same quantity as the number one. Despite having the appearance of representing a smaller number, 0.999... is a symbol for the number 1 in exactly the same way that 0.333... is an equivalent notation for the number represented by the fraction 1 ⁄ 3.
An example of the second case is the decidability of the first-order theory of the real numbers, a problem of pure mathematics that was proved true by Alfred Tarski, with an algorithm that is impossible to implement because of a computational complexity that is much too high. [122]
To convert integer decimals to octal, divide the original number by the largest possible power of 8 and divide the remainders by successively smaller powers of 8 until the power is 1. The octal representation is formed by the quotients, written in the order generated by the algorithm. For example, to convert 125 10 to octal: 125 = 8 2 × 1 + 61
Irish (Standard Irish: Gaeilge), also known as Irish Gaelic or simply Gaelic (/ ˈ ɡ eɪ l ɪ k / ⓘ GAY-lik), [3] [4] [5] is a Celtic language of the Indo-European language family. [4] [6] [7] [8] [3] It is a member of the Goidelic languages of the Insular Celtic sub branch of the family and is indigenous to the island of Ireland. [9]
Beside the Indo-European decimal numeration, there are also remnants of the vigesimal system, as njëzet ' twenty ' and dyzet ' forty '. The Arbëreshë in Italy and Arvanites in Greece may still use trezet ' sixty ' and katërzet ' eighty '. Albanian is the only Balkan language that has preserved the Pre-Indo-European vigesimal system. [142]