Answer: A) The product is rational
Explanation:
The number 4.56 is rational because any terminating decimal can be written as a fraction of two integers. For example, 4.56 = 456/100
The number [tex]4.\overline{5}[/tex] is the same as [tex]4.55555\ldots[/tex] where the '5's go on forever. Repeating decimals like this are rational. It turns out that [tex]\frac{41}{9} = 4.\overline{5} = 4.55555\ldots[/tex] which you can find through trial and error, or apply a bit of algebra. I'll skip showing those steps unless you need me to go over them.
Because both given numbers are rational, multiplying those two rational numbers will lead to another rational number
rational times rational = rational
I'll skip over the proof of this as well unless you need me to show it.
