Question

Please answer number 26

Answer 1

Answer: A) The product is rational

Step-by-step 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
`4.\overline{5}` is the same as
`4.55555\ldots` where the '5's go on forever. Repeating decimals like this are rational. It turns out that
`(41)/(9) = 4.\overline{5} = 4.55555\ldots` 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.