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B How is (4/27)*(3)^3 = 4?

  1. Jan 5, 2016 #1
    How is (4/27)*(3)^3 = 4?

    When I evaluate it as a first step, I reduce the (3)^3 into 9, thus generating:

    (4/27) * 9.

    With a little basic multiplication, I have:
    36/27, or 4/3.
    Which is obviously not equal to 4!

    Am I right or wrong? Where did I make an error?

    Take a look if you please at the answer the author of this article has given as regards the volume of an exemplary cone at the beginning of his page. Did he, or did he not make an error in his final calculation? Or am I wrong? My conclusion is that the volume is 4/3(pi).
     
  2. jcsd
  3. Jan 5, 2016 #2
    3^3 is not equal to 9 (are you thinking of 3*3 ?)
     
  4. Jan 5, 2016 #3
    Oh. Oops. my bad.
     
  5. Jan 5, 2016 #4

    QuantumQuest

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    Gold Member

    A small glitch: 3^3 = 27 not 9. Then answer is indeed 4
     
  6. Jan 6, 2016 #5

    Svein

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    Science Advisor

    Apart from the arithmetic error: This will be wrong if you enter the formula in a C program (or any programming language that handles integers separate from floating point numbers). Assuming 4 and 27 to be integers, 4/27 is 0 (it has to be a non-negative integer less than 1). And even if you do 3^3 as a floating-point calculation, you still have the 0 from the first division...

    Thus: when dealing with integers, (4/27)⋅3^3 ≠ (4⋅3^3)/27!
     
  7. Jan 10, 2016 #6
    5P@N , the multiply and divide operation are an equal priority operation with left associativity. The power is right associative operation and it's priority is higher than multiply and divide operations. Thus the expression can be written as:
    4/27*3^3
    and it is realy equals 4
     
    Last edited by a moderator: Jan 10, 2016
  8. Oct 14, 2016 #7
    ##3^3## is not equal to ##9##

    ##3^3=3×3×3=27##

    ##\dfrac{4}{27}×27\;\;\implies\dfrac{4}{\not27}×\not{27}=4##

    I hope it' ll help.
     
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