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TwiztTiez

  • one year ago

Which number is irrational. A. 0.14 sorry for not knowing math terms and such but there's a bar above the "14" B. 1/3 C. pi 4 D. pi 6

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  1. TwiztTiez
    • one year ago
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    @mathmate

  2. mathmate
    • one year ago
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    Do you know what is an irrational number?

  3. TwiztTiez
    • one year ago
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    Isn't it a number that can be put in decimal form or percentage form?

  4. TwiztTiez
    • one year ago
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    can't*

  5. TwiztTiez
    • one year ago
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    Oops

  6. mathmate
    • one year ago
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    In mathematics, many of the questions can be answered correctly if we know the definition of the terms. If we do not know what the terms mean, the question will appear difficult. So the first step is to understand the meaning of the terms. From wiki: "a rational number is any number that can be expressed as the quotient or fraction p/q of two integers, p and q, with the denominator q not equal to zero." " an irrational number is any real number that cannot be expressed as a ratio of integers. Irrational numbers cannot be represented as terminating or repeating decimals."

  7. mathmate
    • one year ago
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    Are the terms clear to you now?

  8. TwiztTiez
    • one year ago
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    Somewhat

  9. mathmate
    • one year ago
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    For example: (not the same as the first option) 0.14 = 14/100 =7/50, so it can be expressed as a fraction. is it rational?

  10. TwiztTiez
    • one year ago
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    Yes

  11. TwiztTiez
    • one year ago
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    Right?

  12. mathmate
    • one year ago
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    Good!

  13. TwiztTiez
    • one year ago
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    Okay

  14. TwiztTiez
    • one year ago
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    So a number that can become a Fraction or a decimal correct?

  15. mathmate
    • one year ago
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    Now the number 0.13333333333... is called a repeting decimal. It can be converted to a fraction as 2/15

  16. mathmate
    • one year ago
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    All repeting decimals can be converted to a fraction.

  17. TwiztTiez
    • one year ago
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    Oooookay

  18. TwiztTiez
    • one year ago
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    So we're looking for a number that can't be turned into a fraction right?

  19. mathmate
    • one year ago
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    Right! If you need further help, let me know.

  20. TwiztTiez
    • one year ago
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    Oops

  21. TwiztTiez
    • one year ago
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    Option C and D were supposed to be 4 to the fourth and 6 to the fourth

  22. mathmate
    • one year ago
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    I knew there was a typo! So are you all good now?

  23. TwiztTiez
    • one year ago
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    Yes I think it would be D I don't know if I'm correct though

  24. TwiztTiez
    • one year ago
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    @mathmate

  25. mathmate
    • one year ago
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    To avoid communication errors, please give me the answer and not the letter.

  26. TwiztTiez
    • one year ago
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    Oh okay sorry ^-^

  27. TwiztTiez
    • one year ago
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    6 to the fourth

  28. TwiztTiez
    • one year ago
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    You said that repeating decimals can be turned into fractions and A and B are both repeating

  29. TwiztTiez
    • one year ago
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    And 4 to the fourth is 2

  30. TwiztTiez
    • one year ago
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    You there?

  31. TwiztTiez
    • one year ago
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    @mathmate

  32. TwiztTiez
    • one year ago
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    Hello?

  33. TwiztTiez
    • one year ago
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    @campbell_st

  34. campbell_st
    • one year ago
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    well pi is irrational.... so dividing it by anything results in an irrational number.

  35. TwiztTiez
    • one year ago
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    Oh sorry

  36. TwiztTiez
    • one year ago
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    I mistyped earlier

  37. TwiztTiez
    • one year ago
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    4 and 6 are supposed to be put to the fourth

  38. campbell_st
    • one year ago
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    that's ok... I think there are 2 irrational numbers in your answer choices... they both involve pi...

  39. TwiztTiez
    • one year ago
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    Yeah as I said C and D aren't supposed to have Pi

  40. TwiztTiez
    • one year ago
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    They're supposed to be put to the fourth

  41. campbell_st
    • one year ago
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    can you use the draw function to write them

  42. TwiztTiez
    • one year ago
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    \[\sqrt{4} \sqrt{6}\]

  43. campbell_st
    • one year ago
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    I'll let @mathmate continue to answer this

  44. mathmate
    • one year ago
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    @TwiztTiez Remember that all integers are rational, because 5 is the same as 5/1, so it can be represented by a fraction. So the 4 choices are: 1.44444444..... (or 1.4 with a rep. dec. bar) 1/3 4^6 6^6 ? That's why I prefer dealing with the actual numbers, not the choice letters.

  45. mathmate
    • one year ago
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    or rather 1.44444444..... (or 1.4 with a rep. dec. bar) 1/3 4^6 \(\sqrt4 \sqrt6\) which is the same as \(\sqrt{24}\)

  46. mathmate
    • one year ago
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    Which one of these can you NOT represent by a fraction?

  47. TwiztTiez
    • one year ago
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    I didn't mean for it to look like they were supposed to multiplied sorry

  48. mathmate
    • one year ago
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    That's ok, the multiplication is understood. I just used the law of exponents to simplify it.

  49. TwiztTiez
    • one year ago
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    Well \[\sqrt{4} =2\]

  50. mathmate
    • one year ago
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    For your information 1.4444444... equals 13/9.

  51. mathmate
    • one year ago
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    Very good start, continue! So \(\sqrt{4}\sqrt6=2\sqrt{6}\) can you go further?

  52. TwiztTiez
    • one year ago
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    Yup yup

  53. mathmate
    • one year ago
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    I'll put it this way, can you represent \(\sqrt6\) by a fraction?

  54. TwiztTiez
    • one year ago
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    4.8989794

  55. mathmate
    • one year ago
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    ...mathematically exactly?

  56. TwiztTiez
    • one year ago
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    \[2\sqrt{6}=4.8989794...\]

  57. mathmate
    • one year ago
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    2.449489742783178.... and this is not exact.

  58. mathmate
    • one year ago
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    4.898979485566356... and this is not exact.

  59. TwiztTiez
    • one year ago
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    Well how can I make it exact? Is there a way or am I just being oblivious?

  60. TwiztTiez
    • one year ago
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    And I don't mean that rudely

  61. TwiztTiez
    • one year ago
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    Sorry if it came off that way

  62. mathmate
    • one year ago
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    Well, there is no way to represent a square root in decimal form unless it is a perfect square. What does that mean (in the context of this question)?

  63. mathmate
    • one year ago
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    4.89897948556635619639456814941178278393189496131334025686539... and this is still not exact!

  64. TwiztTiez
    • one year ago
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    Oh okay so

  65. TwiztTiez
    • one year ago
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    \[\sqrt{4}=2\]

  66. TwiztTiez
    • one year ago
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    That's exact right?

  67. mathmate
    • one year ago
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    yes, sqrt(4) is rational.

  68. TwiztTiez
    • one year ago
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    Okay I get it

  69. mathmate
    • one year ago
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    but is sqrt(6)?

  70. mathmate
    • one year ago
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    It can be proved mathematically that square root of a number (such as 2, 3, 5,6,...) is not rational unless the number is a perfect square (1,4,9,16,25....)

  71. TwiztTiez
    • one year ago
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    2.44948974278

  72. TwiztTiez
    • one year ago
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    So no I don't think so

  73. mathmate
    • one year ago
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    You can read more about it (and it is interesting reading for general information) at, for example, Wiki: http://en.wikipedia.org/wiki/Irrational_number or http://www.purplemath.com/modules/numtypes.htm

  74. TwiztTiez
    • one year ago
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    Thanks!

  75. mathmate
    • one year ago
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    Correct, since sqrt(6) is not rational, so 2sqrt(6) is also not rational. Does that clear things up a little?

  76. TwiztTiez
    • one year ago
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    It does thanks for the help!

  77. mathmate
    • one year ago
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    Good, you're welcome! :)

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