Suppose you want to divide a real number 547891 by another real number 15888. We can write the two numbers in the form of a polynomial as:

547891 = 5 * 105 + 4 * 104 + 7 * 103 + 8 * 102 + 9 * 101 + 1 * 100 and

15888 = 1 * 104 + 5 * 103 + 8 * 102 + 8 * 101 + 8 * 100, respectively.

In division we can write them as:

547891 / 15888 = 5 * 105 + 4 * 104 + 7 * 103 + 8 * 102 + 9 * 101 + 1 * 100 / 1 * 104 + 5 * 103 + 8 * 102 + 8 * 101 + 8 * 100.

If we remove the number 10 from the division by replacing it with a variable X we can write the above expression as:

5 * X5 + 4 * X4 + 7 * X3 + 8 * X2 + 9 * X1 + 1 * X0 / 1 * X4 + 5 * X3 + 8 * X2 + 8 * X1 + 8 * X0.

We see that two polynomials of degrees 5 and 4 are created in numerator and denominator respectively. Thus division of two real numbers corresponds to division of two polynomials.