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1994 East-Central Regionals of the ACM International Collegiate Programming Contest
Problem F
Expanding Fractions
In this problem you are to print the decimal expansion of a quotient
of two integers. As you well know, the decimal expansions of many
integer quotients result in decimal expansions with repeating
sequences of digits. You must identify these. You will print the
decimal expansion of the integer quotient given, stopping just as the
expansion terminates or just as the repeating pattern is to repeat
itself for the first time. If there is a repeating pattern, you will
say how many of the digits are in the repeating pattern.
Input
There will be multiple input instances, each instance consists of two
positive integers on a line. The first integer represents the
numerator of the fraction and the second represents the
denominator. In this problem, the numerator will always be less than
the denominator and the denominator will be less than 1000. Input
terminates when numerator and denominator are both zero.
Output
For each input instance, the output should consist of the decimal
expansion of the fraction, starting with the decimal point. If the
expansion terminates, you should print the complete decimal
expansion. If the expansion is infinite, you should print the decimal
expansion up to, but not including the digit where the repeated
pattern first repeats itself. For instance, 4/11 = .3636363636...,
should be printed as .36. (Note that the shortest repeating pattern
should be found. In the above example, 3636 and 363636, among others,
are repeating patterns, but the shortest repeating pattern is 36.)
Since some of these expansions may be quite long, multiple line
expansions should each contain exactly 50 characters on each line
(except the last line, which, of course, may be shorter) | that
includes the beginning decimal point. (Helpful hint: The number of
digits before the pattern is repeated will never be more than the
value of the denominator.)
On the line immediately following the last line of the decimal expansion
there should be a line saying either "This expansion terminates.",
or "The last n digits repeat forever.", where n is the number
of digits in the repeating pattern.
Output for each input instance (including the last input instance)
should be followed by a blank line.
Sample Input
3 7
345 800
112 990
53 122
0 0
Sample Output
.428571
The last 6 digits repeat forever.
.43125
This expansion terminates.
.113
The last 2 digits repeat forever.
.4344262295081967213114754098360655737704918032786
885245901639
The last 60 digits repeat forever.
This page maintained by
Ed Karrels.
Last updated September 20, 1999