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Also the converse is true: The decimal expansion of a rational number is either finite, or endlessly repeating. Finite decimal representations can also be seen as a special case of infinite repeating decimal representations. For example, 36 ⁄ 25 = 1.44 = 1.4400000...; the endlessly repeated sequence is the one-digit sequence "0".
Some languages (such as COBOL and PL/I) directly support fixed-point zoned decimal values, assigning an implicit decimal point at some location between the decimal digits of a number. For example, given a six-byte signed zoned decimal value with an implied decimal point to the right of the fourth digit, the hex bytes F1 F2 F7 F9 F5 C0 represent ...
If p and q are primes other than 2 or 5, the decimal representation of the fraction 1 / pq repeats. An example is 1 / 119 : 119 = 7 × 17 λ(7 × 17) = LCM(λ(7), λ(17)) = LCM(6, 16) = 48, where LCM denotes the least common multiple. The period T of 1 / pq is a factor of λ(pq) and it happens to be 48 in this case:
Any such decimal fraction, i.e.: d n = 0 for n > N, may be converted to its equivalent infinite decimal expansion by replacing d N by d N − 1 and replacing all subsequent 0s by 9s (see 0.999...). In summary, every real number that is not a decimal fraction has a unique infinite decimal expansion.
Any such symbol can be called a decimal mark, decimal marker, or decimal sign. Symbol-specific names are also used; decimal point and decimal comma refer to a dot (either baseline or middle ) and comma respectively, when it is used as a decimal separator; these are the usual terms used in English, [ 1 ] [ 2 ] [ 3 ] with the aforementioned ...
The total value of the number is 1 ten, 0 ones, 3 tenths, and 4 hundredths. The zero, which contributes no value to the number, indicates that the 1 is in the tens place rather than the ones place. The place value of any given digit in a numeral can be given by a simple calculation, which in itself is a complement to the logic behind numeral ...
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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 representation with 8 decimal digits could also represent 1.2345678, 1234567.8, 0.000012345678, 12345678000000000, and so on.