A rational number is any number that can be written as the ratio between two other numbers i.e. in the form [tex]\frac{a}{b}[/tex]
Part A:
An easy choice that makes sense is 7.8, right in the middle. To prove that it's rational we need to write it as a ratio. In this case we have [tex]7.8=\frac{78}{10}[/tex]
Part B:
We need a number that can't be written as a ratio (because it neither terminates nor repeats). Some common ones are [tex]\sqrt{2}[/tex], [tex]e[/tex], [tex]\phi[/tex] and [tex]\pi[/tex] so it makes sense to try and use those to build our number. In this case [tex]\frac{11\sqrt{2}}{5}\approx7.78[/tex] works nicely.
