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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 ...
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 ...
For example, the decimal expressions ,,,, represent the fractions 8 / 10 , 1489 / 100 , 79 / 100000 , + 1618 / 1000 and + 314159 / 100000 , and therefore denote decimal fractions. An example of a fraction that cannot be represented by a decimal expression (with a finite number of digits) is 1 / 3 , 3 ...
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 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]
k is a decimal digit and R is a fraction that must be converted to decimal. It usually has only a single digit in the numerator, and one or two digits in the denominator, so the conversion to decimal can be done mentally. Example: find the square root of 75. 75 = 75 × 10 2 · 0, so a is 75 and n is 0.
The advantage of decimal floating-point representation over decimal fixed-point and integer representation is that it supports a much wider range of values. For example, while a fixed-point representation that allocates 8 decimal digits and 2 decimal places can represent the numbers 123456.78, 8765.43, 123.00, and so on, a floating-point ...