calculate the percent of fractions that are repeating vs. non-repeating with R

determine what pecent of fractions are non-repeating.R

# calculate the percent of fractions that are repeating vs. non-repeating

# install stringr if you don't already have it
#install.packages("stringr")

library( stringr )
options( digits=22 )

# this program looks at..
# 1/1, 1/2, 1/3, 1/4.. up to 1/x
# then goes to
# 2/1, 2/2, 2/3, 2/4.. up to 2/x
# and continues increasing the numerator until
# x/1, x/2, x/3, x/4.. up to x/x
# ..and for each of these fractions, determines whether or not it's repeating
# but! any of the above fractions where the numerator is >= the denominator don't count!

percent_repeating_fractions <- function( x ) {
	# create an x by x matrix full of zeroes to store the results
	y <- matrix( 0 , x , x )

	# loop through all natural number numerators & denominators from 1 to x
	for ( numerator in 1:x ){
		for ( denominator in 1:x ){

			# here's the current fraction
			current_fraction <- numerator / denominator

			# throw out matrix cells where the current_fraction is >= 1
			if ( current_fraction >= 1 ) {
				y[ numerator , denominator ] <- NA
			} else {

				# according to http://en.wikipedia.org/wiki/Repeating_decimal
				# a fraction is non-repeating if its denominator is a factor of either two or five
				if (
				
					# use the modulus operator to test for perfect division
					((denominator %% 2) == 0) | 
					((denominator %% 5) == 0)
					
				) {
				
					# mark non-repeating cells with a one
					y[ numerator , denominator ] <- 1
					
				}
			}
		}
	}

	# calculate the number of ones in the final matrix
	ones <- sum( y , na.rm = T )

	# calculate the total number of cells that weren't thrown out
	valid <- sum( !is.na(y) )

	# return the percent of non-repeating fractions out of all fractions tested
	(ones / valid)
}

# run this function for different sized x by x matricies up to z
# choose how high up you want to go (anything above 1000 becomes processor-intensive)
z <- 500

for ( i in 2:z ){
	
	# calculate the percent repeating fractions
	result <- percent_repeating_fractions( i )

	# make the result look nice
	formatted_result <- result * 100
	
	print( 
		paste( 
			"the" ,
			str_pad( i , width = nchar( z ) ) ,
			"by" ,
			str_pad( i , width = nchar( z ) ) ,
			"matrix is" ,
			str_pad( formatted_result , width = 16 , side = "right" ) ,
			"percent non-repeating fractions"
		)
	)
}

# the output makes sense, since out of the denominators ending in 0 through 9,
# denominators 0, 2, 4, 5, 6, and 8 (or 6 out of 10) will be non-repeating

# in conclusion,
# one could argue that about sixty percent of fractions are non-repeating!