long_division <- function(p,q) {
	# fraction p / q

	output <- NULL

	if(q == 0) return(FALSE) # division by zero!
	if(p == 0) return("0")

	r<-p
	if(p<q) {
		# quotient will be less than 1
		r<-10*r
		output <- paste(output, "0.", sep="")
	}
	else
	{
		# quotient will be greater than (or equal) 1
		output <- paste(output, r %/% q, sep="")
		r <- 10*(r %% q)
		if(r>0) output <- paste(output, ".", sep="") else return(output)
	}

	# count prime factors
	cpf <- function(a,b) {
		c <- 0
		while(a%%b==0) {a <- a %/% b; c <- c + 1}
		return(c)
	}

	# greatest common divisor
	gcd <- function(a,b) ifelse (b==0, a, gcd(b, a %% b)) 

	d<-q %/% gcd(p,q)
	len_aperiodic <- max(cpf(d,2), cpf(d,5))
	if(len_aperiodic>0) for(i in 1:len_aperiodic) {
		output <- paste(output, r %/% q, sep="")
		r <- 10*(r %% q)
	}
	remainder <- r
	if(r>0) output <- paste(output, "p", sep="") else return(output)
	while(TRUE) {
		output <- paste(output, r %/% q, sep="")
		r <- 10*(r %% q)
		if(r == remainder) break
	}
	return(output)
}