A solution

DIM N(25)
X = 1.23456
N(0) = INT(X)
A = X - N(0)
w1$ = LTRIM$(STR$(A))
DP = LEN(w1$) - 1
WHILE w1$ <> w2$
J = J + 1
b = 1 / A
N(J) = INT(b)
A = (b - N(J))
L = 0: K = 0
L = N(J) * N(J - 1) + 1
K = N(J)
FOR m = J - 2 TO 1 STEP -1
kk = L
L = L * N(m) + K
K = kk
NEXT m
x1 = INT(((K / L) * 10 ^ DP) + .5)
w2$ = "." + LTRIM$(STR$(x1))
WEND
PRINT X; " = "; L * N(0) + K; "/"; L