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Thread: km-2

  1. #1
    4ania4 is offline Junior Member
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    Default km-2

    Dear Teachers,

    How should I read this :

    3 million tonnes km-2 ?

    Is this the same as the following:

    3 million tonnes/km2 ?

    Thank you for your help,

    4ania4

  2. #2
    emsr2d2's Avatar
    emsr2d2 is offline Moderator
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    Default Re: km-2

    Quote Originally Posted by 4ania4 View Post
    Dear Teachers,

    How should I read this :

    3 million tonnes km-2 ?

    Is this the same as the following:

    3 million tonnes/km2 ?

    Thank you for your help,

    4ania4
    After "3 million tonnes", does it really say "km-2"? I'm not sure if you meant for the letters and numbers in the two versions to be identical, with only the addition of the "slash" in the second. If so, the first is rather unnatural. I would expect to see the slash.

    Three million tonnes per square kilometre.
    Remember - correct capitalisation, punctuation and spacing make posts much easier to read.

  3. #3
    4ania4 is offline Junior Member
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    Default Re: km-2

    Quote Originally Posted by emsr2d2 View Post
    After "3 million tonnes", does it really say "km-2"? I'm not sure if you meant for the letters and numbers in the two versions to be identical, with only the addition of the "slash" in the second. If so, the first is rather unnatural. I would expect to see the slash.

    Three million tonnes per square kilometre.
    Thank you. It must be really rare but I have found a few examples of it in a text on tropical cyclones in Cambridge Academic English Upper Intermediate,

    e.g. In total the passage along a coast can induce a change in load on the Earth's crust of 10 million tonnes km-2.
    Last edited by 4ania4; 11-Apr-2013 at 19:47.

  4. #4
    emsr2d2's Avatar
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    Default Re: km-2

    I have no idea what a "minus square kilometre" is then, if indeed the "dash" is intended to be a minus sign. I think we need a scientist or a maths graduate!
    Remember - correct capitalisation, punctuation and spacing make posts much easier to read.

  5. #5
    SoothingDave is offline VIP Member
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    Default Re: km-2

    Present!

    Note that the negative 2 in the posted example is in superscript. That is, it is an exponent of negative 2, not a subtraction of 2.

    Negative exponents indicate that the value belongs on the bottom of a fraction.

    So it does mean "per square kilometer."

    It's quite unusual in my experience to see negative exponents used like this. Perhaps it was a typesetting decision, but it's strange.

    In my field we see "kg/cm^2" for kilograms per square centimeter. (or "kg/cm2" where it is understood that the "2" is an exponent.)
    Last edited by SoothingDave; 11-Apr-2013 at 23:08. Reason: removed mistaken plural

  6. #6
    4ania4 is offline Junior Member
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    Default Re: km-2

    Thank you so much. Now the meaning is clear to me.

    I think that if you were to read "km-2" aloud, you would just say "per square kilometres". Am I right?
    Last edited by 4ania4; 11-Apr-2013 at 22:45.

  7. #7
    emsr2d2's Avatar
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    Default Re: km-2

    Quote Originally Posted by SoothingDave View Post
    Present!

    Note that the negative 2 in the posted example is in superscript. That is, it is an exponent of negative 2, not a subtraction of 2.

    Negative exponents indicate that the value belongs on the bottom of a fraction.

    So it does mean "per square kilometers."

    It's quite unusual in my experience to see negative exponents used like this. Perhaps it was a typesetting decision, but it's strange.

    In my field we see "kg/cm^2" for kilograms per square centimeter. (or "kg/cm2" where it is understood that the "2" is an exponent.)
    So does "kg/cm^2" mean "the number two should be in superscript but we couldn't do it for some reason"? I have not the first idea what "an exponent of negative 2" means, by the way!
    Remember - correct capitalisation, punctuation and spacing make posts much easier to read.

  8. #8
    Rover_KE is online now Moderator
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    Default Re: km-2

    '...per square kilometre'.

  9. #9
    emsr2d2's Avatar
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    Default Re: km-2

    Quote Originally Posted by 4ania4 View Post
    Thank you so much. Now the meaning is clear to me.

    I think that if you were to read "km-2" aloud, you would just say "per square kilometres". Am I right?
    Singular - per square kilometre.
    Remember - correct capitalisation, punctuation and spacing make posts much easier to read.

  10. #10
    non_e_giusto is offline Newbie
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    Default Re: km-2

    This is mathematics, not English. So as a chemist I dare reply to this thread.

    As stated above, the minus sign indeed means that it is part of the denominator of the fraction, and here is why:

    Let's do some simple exponentiation:

    21 = 2
    22 = 4
    23 = 8
    24 = 16

    You see that every time you add 1 to the exponent, the outcome doubles (exponentiation works like that). But you can also see it the other way around: every time you subtract one from the exponent, you divide by two. So we can do what we just did, but then in reversed order:

    23 = 8
    22 = 4
    21 = 2
    but we don't have to stop here, we can simply keep dividing by 2, so:
    20 = 1
    2-1 = 1/2
    2-2 = 1/4
    2-3 = 1/8

    So what do we see? If you have a negative exponent, it's basically 1 divided by the outcome of the positive exponent (21= 2 and 2-1= 1/2).

    1/2 (2-1) is called the mathematical inverse of 2. The reason is that dividing by 2, is the same thing as multiplying by 1/2 (and vice versa). It also works with symbols: multiplying with s-1 , is the same thing as dividing by s. Scientists use this a lot, because it allows you to neatly write entire fractions in just one line. Instead of meter per second m/s, they write: m s-1 = m * 1/s = m/s

    I hope this is clear, otherwise, ask away.
    Last edited by non_e_giusto; 11-Apr-2013 at 23:17.

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