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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 fractions can also be expressed using scientific notation with negative exponents, ... Thus, it is often useful to convert repeating digits into fractions.
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.
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 ...
If the rational number is a decimal fraction, the division stops eventually, producing a decimal numeral, which may be prolongated into an infinite expansion by adding infinitely many zeros. If the rational number is not a decimal fraction, the division may continue indefinitely.
Scientific calculator displays of fractions and decimal equivalents. Input. ... From there, it is converted by the binary decoder unit into a decimal number ...
If the given number is in decimal and the target base is duodecimal, the method is same. Using the digit conversion tables: (decimal) 10,000 + 2,000 + 300 + 40 + 5 + 0.6 = (duodecimal) 5,954 + 1,1A8 + 210 + 34 + 5 + 0; 7249. To sum these partial products and recompose the number, the addition must be done with duodecimal rather than decimal ...
Working directly with decimal (base-10) fractions can avoid the rounding errors that otherwise typically occur when converting between decimal fractions (common in human-entered data, such as measurements or financial information) and binary (base-2) fractions.