## Marlins0412 Group Title Explain Irrational numbers and give a few examples Thanks! one year ago one year ago

1. inkyvoyd Group Title

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 Group Title

0.394 repeating can be expressed as 394/999

3. Marlins0412 Group Title

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

4. Marlins0412 Group Title

Im studying for my ACT test tomorrow

5. inkyvoyd Group Title

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 Group Title

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

7. Marlins0412 Group Title

give me an example why please

8. inkyvoyd Group Title

Well, pick two numbers between 1 and 10.

9. Marlins0412 Group Title

2 and 7

10. inkyvoyd Group Title

Pick two numbers in between those two.

11. Marlins0412 Group Title

5, 6

12. inkyvoyd Group Title

Now do it again.

13. Marlins0412 Group Title

5.6, 5.7

14. inkyvoyd Group Title

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 Group Title

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

16. Marlins0412 Group Title

so in 1-3 there is many aswell?

17. inkyvoyd Group Title

Well, comparing the two expressions is indeterminant I believe

18. Marlins0412 Group Title

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 Group Title

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

20. inkyvoyd Group Title

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

21. Marlins0412 Group Title

I see

22. Marlins0412 Group Title

WEll off to more studying thanks again

23. inkyvoyd Group Title

yes - good luck!

24. Marlins0412 Group Title

Thanks so much!