Question

Part A: Find a rational number that is between 7.7 and 7.9. Explain why it is rational. (2 points)

Answer 1

A rational number is any number that can be written as the ratio between two other numbers i.e. in the form $\frac{a}{b}$

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 $7.8=\frac{78}{10}$

Part B:
We need a number that can't be written as a ratio (because it neither terminates nor repeats). Some common ones are $\sqrt{2}$, $e$, $\phi$ and $\pi$ so it makes sense to try and use those to build our number. In this case $\frac{11\sqrt{2}}{5}\approx7.78$ works nicely.