Automatic Fractions

[SCM]

The simplest way to do it is find the GCD of the degrees and 180.
In QB it would be something like

Code:

Divisor = GCD( Degrees, 180)
Numerator = Degrees / Divisor
Denominator = 180 / Divisor
Print Numerator; "/"; Divisor; "Pi"

There are ways to convert decimals to fractions, but repeating decimals are handled differently than terminating decimals. You would have to come up with an algorithm to recognise repeating decimals, then handle them appropriately. Examples:

Code:

' Use the same number of 9's as digits in the pattern

0.3333... = 3/9                      ' Repeats one digit.  Use one 9.
          = 1/3

0.142857142857... = 142857/999999    ' Repeats six digits. Use six 9's.
                  = 1/7

' If there is a non-repeating part it has to be handled separately as a terminating decimal,
' and zeros (the same number as the non-repeating part) added after the nines

2.35142857142857... = 2.35 + 0.00142857142857...
                    = 235/100 + 142857/99999900
                    = 235/100 + 1/700
                    = 1645/700 + 1/700
                    = 1646/700
                    =  823/350

[NovaProgramming]

So THAT'S why the calculator couldn't find the GCD of .333333333... ! Would the answer come out the same if the decimal was rounded to #.# instead of .#^n ?

[Agamemnus]

The GCD function needs two numbers. They don't need to be whole numbers. Fraction GCD is the same as any other GCD, except .333333 is not equal to 1/3. 1/3 is equal to 1/3.

Here's a program that I made for a similar question at qbasic.com:

Code:

DECLARE FUNCTION gcd% (n%, m%)
CLS

numerator1% = 2: denominator1% = 5
numerator2% = -3: denominator2% = -5


denominator3% = gcd((denominator1%), (denominator2%))

numerator3% = numerator1% * denominator3% \ denominator1%
numerator3% = numerator3% + numerator2% * denominator3% \ denominator2%

factor2% = gcd((numerator3%), (denominator3%))

IF factor2% = 0 THEN
PRINT "0"
ELSE
numerator3% = numerator3% \ factor2%
denominator3% = denominator3% \ factor2%
IF denominator3% = 1 THEN
PRINT numerator3%
ELSE PRINT LTRIM$(STR$(numerator3%)) + "/" + LTRIM$(STR$(denominator3%))
END IF

END IF

FUNCTION gcd% (n%, m%)
IF m% = 0 THEN EXIT FUNCTION
IF n% = 0 THEN EXIT FUNCTION
'get the GCD
IF m% < n% THEN SWAP m%, n%
DO
r% = m% MOD n%
IF r% = 0 THEN EXIT DO
m% = n%
n% = r%
LOOP
gcd% = n%
END FUNCTION