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how do I do this equation

Discussion in 'Mathematics and Physics' started by north, Jan 12, 2007.

  1. north

    north New Member

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    forgive me for I'm sure this is an easy mathematical question but I'm just starting out in a course called ELECTRO-Mechanical Technician. I just did an exam, my first in this course, but a question has been bugging me.

    the question was 4.91x10^12 electrons are taken out of the flow and then to transfer this into nano. the answer is 787nC.( if I recall accurately).( it is right by the way,787nC, I have the results, but not the specific question, I'm just going by memory)

    this what I thought I should do. since 1 C is 6.24x10^18 electrons. I should subtract 4.91x10^12 from 1C , but in order to do so I have to make the exponents the same> so 4.91x10^12 becomes 4,910,000x10^18 - 6.24x10^18 which does not give the above answer.

    WHAT I"M I DOING WRONG!!
     
    Last edited: Jan 12, 2007
  2. north

    north New Member

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    okay I tried dividing, my only other option, 4.91x10^12 by 6.24x10^18 and I get 7.868589744^29 which is on the right track, but why would I assume that the answer is already in nano's.

    I don't get it. since nano's is 10^9 why wouldn't I say the answer is 7.87x10^20?

    there's something I'm not quite getting here.

    (by the way people I've done the exam already, just in case some may think I'm cheating. cheating in the end only cheats one self)
     
    Last edited: Jan 12, 2007
  3. dknguyen

    dknguyen Well-Known Member

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    Please rephrase this more clearly:
    What is nano?

    BTW:
    (4.91x10^12) / (6.24x10^18) = 786.8589744^-9 (exponents are added when you multiply, subtracted when you divide)

    Try and use some math notation, especially with whacky numbers. It makes it shorter and they don't get lost in the paragraph.

    EDIT: I think I understand your question now. It's basically, how many Coloumbs, do X electrons make right? Well, you said that there are Y electrons/C, and you have X electrons. Therefore you must go
    X/Y = Z[Coloumbs].

    That's the way the units cancel out which verifies it is correct. You are just grouping the electrons into Coloumbs.

    It's like saying, if I have 36, and 12 is a dozen, how many dozens do I have? 36/12 = 3.
     
    Last edited: Jan 12, 2007
  4. dave

    Dave New Member

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  5. north

    north New Member

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    nano is 10^-9


    when I went to ENG on my calculator I got 786.8589744^27.

    have I set my calculator wrong, some how?

    I'm concerned with my ability to interpret what the calculator is actually telling me.
     
    Last edited: Jan 12, 2007
  6. dknguyen

    dknguyen Well-Known Member

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    Well, you should always visually check your numbers to make sure they make sense. I don't use eng mode on my calculator. I have to stay in imaginary numbers for other purposes and I hate how eng mode rounds for me. Does it do it in regular mode?

    Does 10^12/10^10 = 100 on your calulator?
    Does 10^12/10^-10 = 10^22 on your calulator?
    Does 10^-12/10^10 = 10^-22 on your calulator?
    Does 10^-12/10^-10 = 10^-2 on your calulator?

    If so, I'd get a new one...probably a different model. I have no idea what would cause that. What are you using? A TI? Are you sure you aren't just punching it in wrong again and again. I know I've done that before. 6 entries with 6 different numbers every time for me. Had to go to ~13, before I had one answer repeat 3 times.

    When I meant what is nano, I was expecting for you to respond nano-COULOUMBS. That's why I didnt understand your question.
     
    Last edited: Jan 12, 2007
  7. north

    north New Member

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    when I did 10^12/10^10 = 100, that is what I got, 100

    nano-COULOUMBS is what I meant

    thanks for your response by the way. it is appreciated

    north
     
  8. dknguyen

    dknguyen Well-Known Member

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    Huh, weirdness. Oh, I changed my response since I realized that -27 is still not equal to -9, regardless of whether or not the negative sign was burnt out.
     
  9. north

    north New Member

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    let me ask you, how would you do my above problem? never mind my problems with my calculator. just tell me how you would do it your self. and why your answer would be necessarily in nC. to you.

    north
     
  10. hjames

    hjames New Member

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    4.91E12 / 6.42E18 = (4.91/6.42)E(12-18) = .767E-6 = 767E-9 = 767nC
     
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  11. dknguyen

    dknguyen Well-Known Member

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    My answer wouldn't necessarily be in nC. It would be in Couloumbs on some order of magnitude.

    I would think, oh, well I know electrons carry a charge and Coloumb is a unit of charge. I would then think how many many electrons are required to make a charge equal to a Coulomb? Then I'd look in my formula sheet and go oh here it is

    6.24x10^18 electrons / Couloumb

    Then if that's the number, all I have to do is group the electrons up into Couloumbs and count how many groups there are (divide).

    Then I would go:

    4.91x10^12 electrons / (6.24x10^18 electrons / Couloumb)

    = 787 x 10^-9 * (electrons/electrons) * [1 / (1/Couloumbs)]
    = 787 x 10^-9 * 1 * Couloumbs
    = 787 x 10^-9 Couloumbs
    = 787 nC

    You know what I am doing when I divide the units right? You can treat units just like numbers. They divide and all that, even the magnitude prefixes like milli, kilo, or nano can cancel each other out across different units:

    mm/ms = m/s

    It works on any prefix actually as long as you take into account the difference in zeroes.
    km/ms = Mm/s (M = mega)

    It's just a shortcut instead of converting it to the base unit and sticking a "x10^#) at the end. The units must cancel out properly and give you right units at the end or you did something wrong...ALWAYS in every question. It's not hard...you're just getting flustered because it's a test question. Either that, or you don't understand how electrons carry a charge, Couloumbs is a unit of charge, therefore a certain amount of electrons can make a certain Couloumbs of charge.
     
    Last edited: Jan 13, 2007
  12. Pommie

    Pommie Well-Known Member Most Helpful Member

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    (4.91x10^12) / (6.24x10^18) = 786*10^-9

    4.91x10^12 / 6.24x10^18 = 786*10^27

    North, your not entering the numbers correctly.

    Mike.
     
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  13. north

    north New Member

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    everybody thanks for the responses it is appreciated. really!! time though to snooze. I will think and try all points of view. for I must "get it".

    north
     
  14. RODALCO

    RODALCO Well-Known Member

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    Sometimes it is easier to write those values out on paper with all leading or trailing zero's, and space them out in groups of three.
    Then by crossing of zero's get manageable numbers and then do the final part the long way of via calculator.
     
  15. Roff

    Roff Well-Known Member

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    What? I get 787nC.
     
  16. Roff

    Roff Well-Known Member

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    6.42e18 should read 6.24e18, giving an answer of 787nC.
     
  17. dknguyen

    dknguyen Well-Known Member

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    Uhhh....yeah that's what I meant. 7.87 in exponential is what showed up on my calc and I converted it from scientific notation without changing the base. It's been fixed. I've been running on 5 hours less sleep than I'm used to.
     
    Last edited: Jan 13, 2007
  18. north

    north New Member

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    Pommie you are right, once I bracketed the both numbers as you have done above I got 7.866x10^-7 then of course being in nano( in which I had to go 2 decimal places further to the right) the answer came to 787nC. its a relief to get this sorted out!! now I have more confidence with my calculator.

    thanks again, north
     
    Last edited: Jan 14, 2007
  19. Pommie

    Pommie Well-Known Member Most Helpful Member

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    You shouldn't have to enter the brackets. You should have a key to enter the exponent. It is usually labeled E or Exp. So to enter 4.91*10^12 you would enter 4.91E12 or 4.91Exp12.

    Wow, I just went to check on my daughters TI84 and it doesn't have an Exponent key. Calculators seem to have gone backward :confused: I guess that you have to enter the brackets after all.

    Mike.
     
  20. Roff

    Roff Well-Known Member

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    That's why I like my old HP15C (which stays at work). RPN, no parentheses or brackets required.
    The calculator I use here at home when sitting at my computer is an HP41 emulator.
     
  21. Pommie

    Pommie Well-Known Member Most Helpful Member

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    Reverse Polish. :eek: :eek: :eek:
     

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