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The original fraction could have also been reduced in a single step by using the greatest common divisor of 90 and 120, which is 30. As 120 ÷ 30 = 4, and 90 ÷ 30 = 3, one gets = Which method is faster "by hand" depends on the fraction and the ease with which common factors are spotted.
The proof system in the United States was established around 1848 and was based on percent alcohol rather than specific gravity. Fifty percent alcohol by volume was defined as 100 proof. [4] This is different from 50% volume fraction (expressed as a percentage); the latter does not take into account change in volume on mixing, whereas the ...
An example of a fraction that cannot be represented by a decimal expression (with a finite number of digits) is 1 / 3 , 3 not being a power of 10. More generally, a decimal with n digits after the separator (a point or comma) represents the fraction with denominator 10 n, whose numerator is the integer obtained by removing the separator.
The gamma function is an important special function in mathematics.Its particular values can be expressed in closed form for integer and half-integer arguments, but no simple expressions are known for the values at rational points in general.
The harmonic seventh interval, also known as the septimal minor seventh, [2] [3] or subminor seventh, [4] [5] [6] is one with an exact 7:4 ratio [7] (about 969 cents). [8] This is somewhat narrower than and is, "particularly sweet", [9] "sweeter in quality" than an "ordinary" [10] just minor seventh, which has an intonation ratio of 9:5 [11] (about 1018 cents).
If a is replaced with the fraction m/n in the sequence, the result is equal to the 'standard' triple generator (2mn, m 2 − n 2, m 2 + n 2) after rescaling. It follows that every triple has a corresponding rational a value which can be used to generate a similar triangle (one with the same three angles and with sides in the same proportions as ...
Early nuclear physicists used to refer to computing this value as a "packing fraction" calculation. For example, the dalton (1 Da) is defined as 1/12 of the mass of a 12 C atom—but the atomic mass of a 1 H atom (which is a proton plus electron) is 1.007825 Da, so each nucleon in 12 C has lost, on average, about 0.8% of its mass in the form of ...
Most time signatures consist of two numerals, one stacked above the other: The lower numeral indicates the note value that the signature is counting. This number is always a power of 2 (unless the time signature is irrational), usually 2, 4 or 8, but less often 16 is also used, usually in Baroque music. 2 corresponds to the half note (minim), 4 to the quarter note (crotchet), 8 to the eighth ...