Is 9.0832748175... a rational number?
The answer depends on what he ellipsis represents.
Which number can be multiplied to a rational number to explain that the product of two rational numbers is rational?
Actually the product of a nonzero rational number and another rational number will always be rational. The product of a nonzero rational number and an IRrational number will always be irrational. (You have to include the "nonzero" caveat because zero times an irrational number is zero, which is rational)
Why does a rational number plus a rational number or a rational number multiplied by a rational number equal to rational number?
The number 0.444444 is a rational number. It is equivalent to 111111/250000, which, by definition of rational numbers, is rational. The number 0.444... (repeating) is also rational because it can be represented by the fraction 4/9. The number 0.444444 is a rational number because a rational number is a nnumber that can be expressed in the form of a fraction.