Recurring decimals only exist because in the base system we have chosen ( denary-base 10 ), because two integers have been divided and the result is not a terminating decimal.
12.
Every nonzero, terminating decimal ( with infinitely many trailing 0s ) has an equal twin representation with infinitely many trailing 9s ( for example, 8.32 and 8.31999 & ).
13.
The article's claim is just false; " regular number " is not a standard name for a number with a terminating decimal expansion .-- Trovatore 14 : 52, 7 July 2006 ( UTC)
14.
As shown in the section on the existence of Liouville numbers, this number, as well as any other non-terminating decimal with its non-zero digits similarly situated, satisfies the definition of a Liouville number.
15.
If the repetend is a zero, this decimal representation is called a "'terminating decimal "'rather than a repeating decimal, since the zeros can be omitted and the decimal terminates before these zeros.
16.
You could construct such a 1-to-1 mapping between the set of all terminating decimals and the natural numbers, but that would only prove countability of a subset of the rational numbers and so would not be very interesting.
17.
:: : To make a long story short, there is a non-standard representation for every terminating decimal number wherein the final digit is reduced by one and then an infinite string of 9s is appended ( after a decimal point if initially dealing with an integer ).
18.
Every terminating decimal representation can be written as a decimal fraction, a fraction whose divisor is a 0.999 & } } and 1.584999 & } } are two examples of this . ( This type of repeating decimal can be obtained by long division if one uses a modified form of the usual division algorithm .)
19.
A decimal may be a terminating decimal, which has a finite fractional part ( e . g . 15.600 ); a repeating decimal, which has an infinite ( non-terminating ) fractional part made up of a repeating sequence of digits ( e . g . 5.123 144 ); or an infinite decimal, which has a fractional part that neither terminates nor has an infinitely repeating pattern ( e . g . 3.14159265 . . . ).
20.
Exactly one guest would have the address corresponding to one-sixth ( 1-6-6-6 . . . ), for example, and another to the value of pi minus three ( 1-4-1-5 . . . ) . ( Real numbers that have terminating decimal expansions, like 3 / 8 = . 375, actually correspond to two passengers, one with an address ending in an infinite string of zeroes, the other ending in an infinite string of nines.
