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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.
Approximating an irrational number by a fraction π: 22/7 1-digit-denominator Approximating a rational number by a fraction with smaller denominator 399 / 941 3 / 7 1-digit-denominator Approximating a fraction by a fractional decimal number: 5 / 3 1.6667: 4 decimal places: Approximating a fractional decimal number by one with fewer digits 2.1784
Expected fraction of population inside range Expected fraction of population outside range Approx. expected frequency outside range Approx. frequency outside range for daily event μ ± 0.5σ: 0.382 924 922 548 026: 0.6171 = 61.71 % 3 in 5 Four or five times a week μ ± σ: 0.682 689 492 137 086 [5] 0.3173 = 31.73 % 1 in 3 Twice or thrice a ...
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 ...
The McCabe–Thiele method is a technique that is commonly employed in the field of chemical engineering to model the separation of two substances by a distillation column. [ 1 ] [ 2 ] [ 3 ] It uses the fact that the composition at each theoretical tray is completely determined by the mole fraction of one of the two components.
In mathematics, "rational" is often used as a noun abbreviating "rational number". The adjective rational sometimes means that the coefficients are rational numbers. For example, a rational point is a point with rational coordinates (i.e., a point whose coordinates are rational numbers); a rational matrix is a matrix of rational numbers; a rational polynomial may be a polynomial with rational ...
Conversely the period of the repeating decimal of a fraction c / d will be (at most) the smallest number n such that 10 n − 1 is divisible by d. For example, the fraction 2 / 7 has d = 7, and the smallest k that makes 10 k − 1 divisible by 7 is k = 6, because 999999 = 7 × 142857. The period of the fraction 2 / 7 is ...
The smallest (and unique up to rotation and reflection) non-trivial case of a magic square, order 3. In mathematics, especially historical and recreational mathematics, a square array of numbers, usually positive integers, is called a magic square if the sums of the numbers in each row, each column, and both main diagonals are the same.