Is 7.8 a rational number

Yes, it is. Because you can write it in the form of p/q as

78/10

= 39/5

Yes, any number that can be represented as a ratio of two integers is rational ...

7.8

7 8/10

78/10

39/5

You can also be aware that any terminating number (including terminating decimals) or any number with a repeating decimal pattern is rational.