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They are irrational because if you tried to describe either of these numbers it would go on forever. As soon as you thought you were done, you’d would have to be more specific, adding more …5’s or …15’s. These numbers are what can be said to be “infinitely precise”. So trying to explain something which extends to infinity is difficult to do.

Maybe a good way for you to think about it is if it would make sense to try to describe the number to someone. How would you describe 0.5? You’d say 1/2. And 0.1? You’d say one tenth. But trying to describe 0.55555….? The only way you could it would be to sit there forever saying “…five…”, “…five…”, “…five…”. That would not be a sensible thing to do. That would be irrational.

I found this question to be good question and quite a difficult one to explain outside a math text book, even having a minor in mathematics (though I don’t really use it).

I hope that helps, imaginary and irrational numbers can be difficult to grasp.

To write a number as a fraction you have to divide the first number after the decimal by 10, or the first two numbers by 100, or the first three numbers by 1000, etc. Then simplify if you have to.

Therefore for (1), that is a rational number. To get a fraction it’s 5/10, which you can then simplify. I’ll let you do the rest…

An irrational number is any real number that is not a rational number — that is, it is a number which cannot be expressed as a fraction a/b.

So here we go…. assuming you know how to get fractions from decimals…

1. .5 = 1/2 <---Rational 2. .555555 = you can not make a simple fraction, therefore it is Irrational 3. .1 = 1/10 <----Rational 4. .151515 = it will continue on forever, just like number 2 making it irrational, because it cannot be explained by a fraction.