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

1. TwiztTiez

@mathmate

2. mathmate

Do you know what is an irrational number?

3. TwiztTiez

Isn't it a number that can be put in decimal form or percentage form?

4. TwiztTiez

can't*

5. TwiztTiez

Oops

6. mathmate

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

Are the terms clear to you now?

8. TwiztTiez

Somewhat

9. mathmate

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

Yes

11. TwiztTiez

Right?

12. mathmate

Good!

13. TwiztTiez

Okay

14. TwiztTiez

So a number that can become a Fraction or a decimal correct?

15. mathmate

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

16. mathmate

All repeting decimals can be converted to a fraction.

17. TwiztTiez

Oooookay

18. TwiztTiez

So we're looking for a number that can't be turned into a fraction right?

19. mathmate

Right! If you need further help, let me know.

20. TwiztTiez

Oops

21. TwiztTiez

Option C and D were supposed to be 4 to the fourth and 6 to the fourth

22. mathmate

I knew there was a typo! So are you all good now?

23. TwiztTiez

Yes I think it would be D I don't know if I'm correct though

24. TwiztTiez

@mathmate

25. mathmate

To avoid communication errors, please give me the answer and not the letter.

26. TwiztTiez

Oh okay sorry ^-^

27. TwiztTiez

6 to the fourth

28. TwiztTiez

You said that repeating decimals can be turned into fractions and A and B are both repeating

29. TwiztTiez

And 4 to the fourth is 2

30. TwiztTiez

You there?

31. TwiztTiez

@mathmate

32. TwiztTiez

Hello?

33. TwiztTiez

@campbell_st

34. campbell_st

well pi is irrational.... so dividing it by anything results in an irrational number.

35. TwiztTiez

Oh sorry

36. TwiztTiez

I mistyped earlier

37. TwiztTiez

4 and 6 are supposed to be put to the fourth

38. campbell_st

that's ok... I think there are 2 irrational numbers in your answer choices... they both involve pi...

39. TwiztTiez

Yeah as I said C and D aren't supposed to have Pi

40. TwiztTiez

They're supposed to be put to the fourth

41. campbell_st

can you use the draw function to write them

42. TwiztTiez

$\sqrt{4} \sqrt{6}$

43. campbell_st

I'll let @mathmate continue to answer this

44. mathmate

@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

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

Which one of these can you NOT represent by a fraction?

47. TwiztTiez

I didn't mean for it to look like they were supposed to multiplied sorry

48. mathmate

That's ok, the multiplication is understood. I just used the law of exponents to simplify it.

49. TwiztTiez

Well $\sqrt{4} =2$

50. mathmate

For your information 1.4444444... equals 13/9.

51. mathmate

Very good start, continue! So $$\sqrt{4}\sqrt6=2\sqrt{6}$$ can you go further?

52. TwiztTiez

Yup yup

53. mathmate

I'll put it this way, can you represent $$\sqrt6$$ by a fraction?

54. TwiztTiez

4.8989794

55. mathmate

...mathematically exactly?

56. TwiztTiez

$2\sqrt{6}=4.8989794...$

57. mathmate

2.449489742783178.... and this is not exact.

58. mathmate

4.898979485566356... and this is not exact.

59. TwiztTiez

Well how can I make it exact? Is there a way or am I just being oblivious?

60. TwiztTiez

And I don't mean that rudely

61. TwiztTiez

Sorry if it came off that way

62. mathmate

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

4.89897948556635619639456814941178278393189496131334025686539... and this is still not exact!

64. TwiztTiez

Oh okay so

65. TwiztTiez

$\sqrt{4}=2$

66. TwiztTiez

That's exact right?

67. mathmate

yes, sqrt(4) is rational.

68. TwiztTiez

Okay I get it

69. mathmate

but is sqrt(6)?

70. mathmate

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

2.44948974278

72. TwiztTiez

So no I don't think so

73. mathmate

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

Thanks!

75. mathmate

Correct, since sqrt(6) is not rational, so 2sqrt(6) is also not rational. Does that clear things up a little?

76. TwiztTiez

It does thanks for the help!

77. mathmate

Good, you're welcome! :)