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To change 1 / 3 to a decimal, divide 1.000... by 3 (" 3 into 1.000... "), and stop when the desired accuracy is obtained, e.g., at 4 decimals with 0.3333. The fraction 1 / 4 can be written exactly with two decimal digits, while the fraction 1 / 3 cannot be written exactly as a decimal with a finite number of digits.
A fixed-point representation of a fractional number is essentially an integer that is to be implicitly multiplied by a fixed scaling factor. For example, the value 1.23 can be stored in a variable as the integer value 1230 with implicit scaling factor of 1/1000 (meaning that the last 3 decimal digits are implicitly assumed to be a decimal fraction), and the value 1 230 000 can be represented ...
The partial sums of the series 1 + 2 + 3 + 4 + 5 + 6 + ⋯ are 1, 3, 6, 10, 15, etc.The nth partial sum is given by a simple formula: = = (+). This equation was known ...
(However, PE only dissolves at temperatures well above 100 °C.) Poly(styrene) has a solubility parameter of 9.1 cal 1/2 cm −3/2, and thus ethyl acetate is likely to be a good solvent. Nylon 6,6 has a solubility parameter of 13.7 cal 1/2 cm −3/2, and ethanol is likely to be the best solvent of those tabulated. However, the latter is polar ...
Division is one of the four basic operations of arithmetic. The other operations are addition, subtraction, and multiplication. What is being divided is called the dividend, which is divided by the divisor, and the result is called the quotient. At an elementary level the division of two natural numbers is, among other possible interpretations ...
The square root of 2 (approximately 1.4142) is a real number that, when multiplied by itself or squared, equals the number 2. It may be written in mathematics as or . It is an algebraic number, and therefore not a transcendental number.
In mathematics, the harmonic series is the infinite series formed by summing all positive unit fractions : The first terms of the series sum to approximately , where is the natural logarithm and is the Euler–Mascheroni constant. Because the logarithm has arbitrarily large values, the harmonic series does not have a finite limit: it is a ...
The idea becomes clearer by considering the general series 1 − 2x + 3x 2 − 4x 3 + 5x 4 − 6x 5 + &c. that arises while expanding the expression 1 ⁄ (1+x) 2, which this series is indeed equal to after we set x = 1.