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Let x = the repeating decimal: x = 0.1523 987; Multiply both sides by the power of 10 just great enough (in this case 10 4) to move the decimal point just before the repeating part of the decimal number: 10,000x = 1,523. 987; Multiply both sides by the power of 10 (in this case 10 3) that is the same as the number of places that repeat:
Qin Jiushao's book Mathematical Treatise in Nine Sections (1247) explicitly writes a decimal fraction representing a number rather than a measurement, using counting rods. [29] The number 0.96644 is denoted 寸. Historians of Chinese science have speculated that the idea of decimal fractions may have been transmitted from China to the Middle ...
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 ...
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: 2.18 2 decimal places Approximating a decimal integer by an integer with more trailing zeros 23217: 23200: 3 significant figures Approximating a large decimal integer using ...
Decimal expansion Continued fraction Notes Zero: 0 ... 3, 13, 5, 1, 1, 8, 1, 2, 4, 1 ... the coefficients of the continued fraction of x have a finite geometric mean ...
Every terminating decimal representation can be written as a decimal fraction, a fraction whose denominator is a power of 10 (e.g. 1.585 = 1585 / 1000 ); it may also be written as a ratio of the form k / 2 n ·5 m (e.g. 1.585 = 317 / 2 3 ·5 2 ).
By default, the output value is rounded to adjust its precision to match that of the input. An input such as 1234 is interpreted as 1234 ± 0.5, while 1200 is interpreted as 1200 ± 50, and the output value is displayed accordingly, taking into account the scale factor used in the conversion.
Most decimal fractions (or most fractions in general) cannot be represented exactly as a fraction with a denominator that is a power of two. For example, the simple decimal fraction 0.3 (3 ⁄ 10) might be represented as 5404319552844595 ⁄ 18014398509481984 (0.299999999999999988897769…). This inexactness causes many problems that are ...