Is 1.7777777 a irrational number

Well, honey, let me break it down for you. If you're talking about the decimal 1.7777777, then no, that's a rational number because it can be expressed as 8/9. But if you're referring to the infinite string of 7's, then yes, that's irrational because it can't be expressed as a simple fraction. So, it really depends on which 1.7777777 you're talking about, sugar.