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Thus, it is often useful to convert repeating decimals into fractions. A conventional way to indicate a repeating decimal is to place a bar (known as a vinculum) over the digits that repeat, for example 0. 789 = 0.789789789... For repeating patterns that begin immediately after the decimal point, the result of the conversion is the fraction ...
In order to convert a rational number represented as a fraction into decimal form, one may use long division. For example, consider the rational number 5 / 74 : 0.0 675 74 ) 5.00000 4.44 560 518 420 370 500 etc. Observe that at each step we have a remainder; the successive remainders displayed above are 56, 42, 50.
Decimal degrees (DD) is a notation for expressing latitude and longitude geographic coordinates as decimal fractions of a degree. DD are used in many geographic information systems (GIS), web mapping applications such as OpenStreetMap , and GPS devices.
Every decimal representation of a rational number can be converted to a fraction by converting it into a sum of the integer, non-repeating, and repeating parts and then converting that sum to a single fraction with a common denominator.
To calculate a percentage of a percentage, convert both percentages to fractions of 100, or to decimals, and multiply them. For example, 50% of 40% is: 50 / 100 × 40 / 100 = 0.50 × 0.40 = 0.20 = 20 / 100 = 20%. It is not correct to divide by 100 and use the percent sign at the same time; it would literally imply ...
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 ...
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 ...
Decimal fractions were first developed and used by the Chinese in the form of rod calculus in the 1st century BC, and then spread to the rest of the world. [6] [7] J. Lennart Berggren notes that positional decimal fractions were first used in the Arab by mathematician Abu'l-Hasan al-Uqlidisi as early as the 10th century. [8]