flaming_ninja said:
0.9*recurring is not equal to 1 because no matter how infinitesimally small the difference is, the difference exists.
10 * 0.9*recurring = 9.9*recurring. (simply switch the decimal point one place as always when multiplying by ten)
9.9*recurring - 0.9*recurring = 9. (beyond the decimal point these numbers are identical.)
10 * 0.9*recurring - 0.9*recurring = 9 * 0.9*recurring = 9. (10 * a - a = 9 * a. By the definition of multiplication.)
9 * 0.9*recurring = 9 * 1.
0.9*recurring = 1.
No difference at all. Not even an infinitely small one.