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Thread: Really long number problem

  1. #1 Really long number problem 
    Forum Professor leohopkins's Avatar
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    Hi guys,

    I have to solve a problem. I have a Texas Instruments TI-84plus calculator, and im trying to use very big and small (long) numbers.

    Okay, this is the calculation im trying to do:

    3819718.635 N/m^2 / 210000000000 N/m^2 (giga newtons basically)

    Anyway, the calculator hits me back with:

    1.818913636E^-5

    Does anyone have any idea how to read this ? If you do please let me know; also, is there an online calculator ANYWHERE on the net where i can use really long numbers and not get back, what to me is seemingly garbage :s

    Any help would be great. Thanks :-)


    The hand of time rested on the half-hour mark, and all along that old front line of the English there came a whistling and a crying. The men of the first wave climbed up the parapets, in tumult, darkness, and the presence of death, and having done with all pleasant things, advanced across No Man's Land to begin the Battle of the Somme. - Poet John Masefield.

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  3. #2  
    Moderator Moderator AlexP's Avatar
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    It's just simple scientific notation. It equals 0.00001818913636. The E is just what the TI uses instead of "times 10 to the." So E<sup>-5</sup> means x 10<sup>-5</sup>, so you move the decimal 5 places to the left.


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  4. #3  
    Forum Professor leohopkins's Avatar
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    Aha. Okay thanks.

    Although that doesnt seem to make sense to me, perhaps it is because my calculations are wrong but......

    When trying to calculate how thick a piece of steel cable needs to be in order to be strong enough to withstand a maximum load of 90,000 newtons and this particular steel has a stress failure at 1200MN m^2 I have used the following calculation:

    (in SI)

    90000 / 1200,000,000 = 7.5E^-5

    Which would mean 0.00075m^2 which makes little to no sense
    The hand of time rested on the half-hour mark, and all along that old front line of the English there came a whistling and a crying. The men of the first wave climbed up the parapets, in tumult, darkness, and the presence of death, and having done with all pleasant things, advanced across No Man's Land to begin the Battle of the Somme. - Poet John Masefield.

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  5. #4  
    Forum Masters Degree organic god's Avatar
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    well the steel does have a very high stress failure.

    so therefore the c.s.a doesn't need to be lage to withstand large forces
    everything is mathematical.
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  6. #5  
    Forum Professor leohopkins's Avatar
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    Sure I understand. Now im going to seem thick, but what would the diameter of a circle be (in millimetres) if the area is 0.00075m^2. My backwards calculation of Pi x R^2 isnt seeming to help
    The hand of time rested on the half-hour mark, and all along that old front line of the English there came a whistling and a crying. The men of the first wave climbed up the parapets, in tumult, darkness, and the presence of death, and having done with all pleasant things, advanced across No Man's Land to begin the Battle of the Somme. - Poet John Masefield.

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  7. #6  
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    area = pi*r^2 like you said

    diameter = 2*r

    area = pi*(d/2)^2

    = (pi*d^2)/4

    d = sqrt (4*area/pi)
    everything is mathematical.
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    Be careful, 7.5E<sup>-5</sup> = 0.000075, not 0.00075.
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  9. #8  
    Forum Professor leohopkins's Avatar
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    Oh I see, so........ can you double check the arithmatic on this for me please.....

    if the area of the cable is indeed 0.000075m^2 then:

    diameter = squareroot(4*0.000075/Pi)

    Which equals: 0.0097720502m or rounded and using milimetres: 98mm ??
    The hand of time rested on the half-hour mark, and all along that old front line of the English there came a whistling and a crying. The men of the first wave climbed up the parapets, in tumult, darkness, and the presence of death, and having done with all pleasant things, advanced across No Man's Land to begin the Battle of the Somme. - Poet John Masefield.

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    No, 0.0098 m would be 9.8 mm.

    You asked about an online calculator. Have you tried the Google calculator? Just type your formula into the Google search box as if you were searching the internet. It will also do unit conversions. Example: type

    7.5 meters per 80 seconds in furlongs per fortnight

    And you get:

    (7.5 meters) per (80 seconds) = 563.707946 furlongs per fortnight
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    I doubt there are a lot of calculators with more than 16 digits, since it is rarely useful to have more. (The only reason I can think of is to calculate a lot of digits of pi or to find a very small difference between two very accurate large values).

    In your case, just calculate 3.8e6/2.1e11 which gives 1.8e-5. (where 6-11=-5)
    The Young's Modulus isn't much more accurate than that anyway.

    If you really need a large amount of digits, a very expensive mathematical program such as Maple can do it (I used it to calculate 2 million digits for pi once for fun).
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  12. #11  
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    Quote Originally Posted by Harold14370
    No, 0.0098 m would be 9.8 mm.

    You asked about an online calculator. Have you tried the Google calculator? Just type your formula into the Google search box as if you were searching the internet. It will also do unit conversions. Example: type

    7.5 meters per 80 seconds in furlongs per fortnight

    And you get:

    (7.5 meters) per (80 seconds) = 563.707946 furlongs per fortnight
    Oh yes, duh. Oh dear - i can see its going to take a while to get this old brain working again :s
    The hand of time rested on the half-hour mark, and all along that old front line of the English there came a whistling and a crying. The men of the first wave climbed up the parapets, in tumult, darkness, and the presence of death, and having done with all pleasant things, advanced across No Man's Land to begin the Battle of the Somme. - Poet John Masefield.

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  13. #12  
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    Quote Originally Posted by Bender
    If you really need a large amount of digits, a very expensive mathematical program such as Maple can do it (I used it to calculate 2 million digits for pi once for fun).
    Or you can use the free trial version of Derive.
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    Alas, I cannot shine any alternative light upon this discussion; hence, I have a question: Am I right to think that Pi has 157 decimal places? Or is it an infinite number?
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    Out of curiosity, where did you get the number 157 from? Anyway, no, pi cannot be expressed in any finite number of digits in any base.
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    Out of curiosity, where did you get the number 157 from? Anyway, no, pi cannot be expressed in any finite number of digits in any base
    mechanical engineers "pi is about 3"
    everything is mathematical.
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    Quote Originally Posted by organic god
    mechanical engineers "pi is about 3"
    Depends. In strength calculations: yes, but in a lot of other applications, inducing an error of 5% like that is simply unacceptable. 8) We're working submicron nowadays.

    I am wondering about the the origin of the 157 digits of pi. And hypothetically, could you take an irrational base in which pi could have only a limited amount of digits? Not very practical if every other number is irrational. I think in base pi, 10 would be 100.0102... but something tells me there has to be a reason why you can't take an irrational number as a base.
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  18. #17  
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    Quote Originally Posted by MagiMaster
    Out of curiosity, where did you get the number 157 from? Anyway, no, pi cannot be expressed in any finite number of digits in any base.

    Hmmm im not so sure about that tbh.

    We have calculated pi so far to well over a million decimals, but that doesnt mean it IS infinate, it COULD be but we don't know do we ? - There is a very good reason as to why i doubt its infinity and that is with each proceeding decimal you are making smaller and smaller dimension shift's right. Well, sooner or later you are going to come accross a supposed shift that could be smaller than a singulrity. - You see, i dont buy it, but like i said we will probably never know (unless a quantum computer can be built to try and compute it to well beyond a trilllion trillion decimals.
    The hand of time rested on the half-hour mark, and all along that old front line of the English there came a whistling and a crying. The men of the first wave climbed up the parapets, in tumult, darkness, and the presence of death, and having done with all pleasant things, advanced across No Man's Land to begin the Battle of the Somme. - Poet John Masefield.

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    All rational numbers have a repeating or terminating decimal expansion. Conversely, any repeating/terminating decimal expansion represents a rational number. Since is irrational (yes, it has been proved to be irrational – in fact, it has been proved to be not only irrational but transcendental) the decimal expansion of is therefore non-repeating and non-terminating. This has nothing to do with scales or “dimension shift” (whatever that is).
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  20. #19  
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    Quote Originally Posted by Bender
    Quote Originally Posted by organic god
    mechanical engineers "pi is about 3"
    Depends. In strength calculations: yes, but in a lot of other applications, inducing an error of 5% like that is simply unacceptable. 8) We're working submicron nowadays.

    I am wondering about the the origin of the 157 digits of pi. And hypothetically, could you take an irrational base in which pi could have only a limited amount of digits? Not very practical if every other number is irrational. I think in base pi, 10 would be 100.0102... but something tells me there has to be a reason why you can't take an irrational number as a base.
    You could in principle represent real numbers in terms of an infinite series in powers of 1/pi, just like we represent in base 10 in powers of 1/10. In that system pi would be represented by 1.

    But that does not make pi a rational number, or even an algebraic number. What is does is just confuse the hell out of things. Pi has simple decimal representation, but 1 will be a first class mess.

    That is why discussions of bases are usually restricted to natural numbers. Once can conceive of "natural" representations in any natural number base, and base 2 is , as you know, the base of choice for digital computers. Other bases are unnatural and so ugly that there is not point in using them.

    "God made the integers, all else is the work of man." – Leopold Kronecker
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  21. #20  
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    Quote Originally Posted by DrRocket
    You could in principle represent real numbers in terms of an infinite series in powers of 1/pi, just like we represent in base 10 in powers of 1/10. In that system pi would be represented by 1.

    But that does not make pi a rational number, or even an algebraic number. What is does is just confuse the hell out of things. Pi has simple decimal representation, but 1 will be a first class mess.

    That is why discussions of bases are usually restricted to natural numbers. Once can conceive of "natural" representations in any natural number base, and base 2 is , as you know, the base of choice for digital computers. Other bases are unnatural and so ugly that there is not point in using them.

    "God made the integers, all else is the work of man." – Leopold Kronecker
    I know it's messy, and I can't see a practical use, I just wondered whether I was missing something about it being possible. BTW, wouldn't pi be represented as 10, and 1 as 1 or .

    I guess a big problem with an non-integer base is the non-exclusiveness of numbers: 1 in base pi could be 1 or 0.2312... or 0.3011... etc...
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  22. #21  
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    Quote Originally Posted by Bender
    know it's messy, and I can't see a practical use, I just wondered whether I was missing something about it being possible. BTW, wouldn't pi be represented as 10, and 1 as 1 or .

    I guess a big problem with an non-integer base is the non-exclusiveness of numbers: 1 in base pi could be 1 or 0.2312... or 0.3011... etc...
    You are right about the representation of pi as 10 and 1 as 1. But with decimal representations there is some non-uniqueness. In base 10 you can also represent 1 as 0.999999999... and in base 2 as 0.1111111111...

    The means for representing numbers is not nearly as important as the concepts of the numbers themselves. One is still one, no matter how it is represented. And representing in powers of pi might be possible, but that doesn't make it a good idea. In fact, since we have no particularly good representation of pi as a decimal, representing 5 could be quite a challenge. Can you imagine a clerk in a store trying to make change for payment with a $5 bill used to purchase a pack of gum in base pi ?

    I prefer the exact representation of pi -- .
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