(Another small note.... 1.25 * 0.1 is not representable because 0.1 is not representable, so that doesn't divide by 10)

1.25 = 2^0 + 2^-2, so is representable.

0.125 = 2^-3, so is representable

1.25 / 10.0 = 0.125 so is representable. 10.0 = 2^3 + 2^1.

1.25 * 0.1 is not representable, because 0.1 is not representable, and those low order bits show up in the multiplication