Help with Rational and Irrational Problems

Question

anonymous · Answer

attachment

anonymous · Answer

@phi

phi · Answer

the good news is its either rational or irrational  (no mixture)
so you can rule out any answer  that says otherwise.

anonymous · Answer

its rational

phi · Answer

the "trick" to recognize rational numbers with decimals is that the if you can list the digits that repeat, it's rational

example.  0.15 with a line over 0.15  means 0.151515.... and so on
the 15 repeats, which means rational
ditto for 0.6666...

phi · Answer

an example if irrational is 
pi = 3.14159.... there is *no pattern*  and you can't guess the next digit unless you calculate.  that is different from 0.151515... where we know the next digits are 15 and so on.