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Marlins0412

  • 2 years ago

Explain Irrational numbers and give a few examples Thanks!

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  1. inkyvoyd
    • 2 years ago
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    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
    • 2 years ago
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    0.394 repeating can be expressed as 394/999

  3. Marlins0412
    • 2 years ago
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    ok so how many irrational numbers are from 1-10?

  4. Marlins0412
    • 2 years ago
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    Im studying for my ACT test tomorrow

  5. inkyvoyd
    • 2 years ago
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    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
    • 2 years ago
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    There are an infinite number of rational AND irrational numbers between 1-10...

  7. Marlins0412
    • 2 years ago
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    give me an example why please

  8. inkyvoyd
    • 2 years ago
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    Well, pick two numbers between 1 and 10.

  9. Marlins0412
    • 2 years ago
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    2 and 7

  10. inkyvoyd
    • 2 years ago
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    Pick two numbers in between those two.

  11. Marlins0412
    • 2 years ago
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    5, 6

  12. inkyvoyd
    • 2 years ago
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    Now do it again.

  13. Marlins0412
    • 2 years ago
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    5.6, 5.7

  14. inkyvoyd
    • 2 years ago
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    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
    • 2 years ago
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    There are actually "far more" irrational numbers than rational numbers.

  16. Marlins0412
    • 2 years ago
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    so in 1-3 there is many aswell?

  17. inkyvoyd
    • 2 years ago
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    Well, comparing the two expressions is indeterminant I believe

  18. Marlins0412
    • 2 years ago
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    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
    • 2 years ago
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    @Marlins0412 , the key thing to know is that there are an infinite number of rational and irrational numbers

  20. inkyvoyd
    • 2 years ago
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    rational numbers can be expressed as the division of two integers, while irrational numbers cannot

  21. Marlins0412
    • 2 years ago
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    I see

  22. Marlins0412
    • 2 years ago
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    WEll off to more studying thanks again

  23. inkyvoyd
    • 2 years ago
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    yes - good luck!

  24. Marlins0412
    • 2 years ago
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    Thanks so much!

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