## Marlins0412 2 years ago Explain Irrational numbers and give a few examples Thanks!

1. inkyvoyd

A rational number is a number that can be expressed as the ratio of two integers. For instance, 0.5 is a rational number, which is 1/2

2. inkyvoyd

0.394 repeating can be expressed as 394/999

3. Marlins0412

ok so how many irrational numbers are from 1-10?

4. Marlins0412

Im studying for my ACT test tomorrow

5. inkyvoyd

However, in the defined "real number set", not all numbers can be expressed as the division of two integers. Although historically it took a bit of time for us to accept this, a simple proof of the the fact that $$\sqrt{2}$$ is irrational is suffice

6. inkyvoyd

There are an infinite number of rational AND irrational numbers between 1-10...

7. Marlins0412

give me an example why please

8. inkyvoyd

Well, pick two numbers between 1 and 10.

9. Marlins0412

2 and 7

10. inkyvoyd

Pick two numbers in between those two.

11. Marlins0412

5, 6

12. inkyvoyd

Now do it again.

13. Marlins0412

5.6, 5.7

14. inkyvoyd

an important property of the real numbers is that they are continuous - in a sense, there are an INFINITE "number" of numbers in between any two different numbers, no matter how small the difference

15. inkyvoyd

There are actually "far more" irrational numbers than rational numbers.

16. Marlins0412

so in 1-3 there is many aswell?

17. inkyvoyd

Well, comparing the two expressions is indeterminant I believe

18. Marlins0412

Great! Thanks a lot for your help it cleared my confusion. Hopefully I get this right on one of the biggest tests of my life!

19. inkyvoyd

@Marlins0412 , the key thing to know is that there are an infinite number of rational and irrational numbers

20. inkyvoyd

rational numbers can be expressed as the division of two integers, while irrational numbers cannot

21. Marlins0412

I see

22. Marlins0412

WEll off to more studying thanks again

23. inkyvoyd

yes - good luck!

24. Marlins0412

Thanks so much!