Answer:
Step-by-step explanation:
This is a super question. The ancient Greeks knew about irrationals but because they were so weird, the Greeks decided that they were not numbers. I get the feeling students would agree with them.
A rational number is any number that can be represented as a fraction. 5/7 therefore is a rational number. So is 139 / 293 No matter how miserable the fraction is, eventually it will repeat.
Take 1/7 as an example 1/7 = 0.142857 The next number is a 1. The number after the 1 is a 4 and so on. So if I told you that the 5 occupies the place we are talking about, you'd be able to tell me that the next digit is a 7. 1/7 is rational which in plain talk 1/7 is well behaved.
The irrationals cannot be represented as a fraction. sqrt(5) is totally irrational. If I told you that the hundredth digit is a 5 (and I don't know if it is) you have a 1 in 10 chance of guessing the next number. Only a computer has the ability to figure out such a monster easily.
Leave a question if you don't understand. It will show up in my comments and I'll try and clear up the problem.
