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Confusing powers

  • 08-01-2011 06:37PM
    #1
    thecatspjs
    Closed Accounts Posts: 519 ✭✭✭


    Is 0.27x10^-6 meters cubed the same as 0.27 cm cubed?
    Just doin some problems here and can't get my head around this for some reason


Comments

  • #2
    FarmerGreen
    Registered Users, Registered Users 2 Posts: 1,134 ✭✭✭FarmerGreen


    0.27 micrometers? 10^-6= one millionth.


  • #3
    Michael Collins
    Moderators, Science, Health & Environment Moderators Posts: 1,855 Mod ✭✭✭✭Michael Collins


    thecatspjs wrote: »
    Is 0.27x10^-6 meters cubed the same as 0.27 cm cubed?
    Just doin some problems here and can't get my head around this for some reason

    Yes,

    [latex] \displaystyle 0.27 \times 10^{-6} \cdot \hbox{m^3} [/latex]

    100 cm in every m, so

    [latex] \displaystyle 0.27 \times 10^{-6} \cdot (100 \; \hbox{cm})^3 [/latex]

    [latex] \displaystyle 0.27 \times 10^{-6} \cdot (100^3 \; \hbox{cm}^3) [/latex]

    [latex] \displaystyle 0.27 \times 10^{-6} \cdot 10^6 \; \hbox{cm}^3 [/latex]

    [latex] \displaystyle 0.27 \; \hbox{cm^3} [/latex]


  • #4
    FISMA
    Closed Accounts Posts: 2,616 ✭✭✭FISMA


    Do you want to cube the whole lot - [0.27x10^-6 meters]^3?

    [0.27x10^-6 meters]^3 = 1.97x10-14 cm^3

    But if you meant to convert [0.27x10^-6 ] meters^3? to cm^3 then as demonstrated by the Big Fella

    [0.27x10^-6 ] meters^3? = 0.27cm^3 - true because in one cubic meter there are one million centimeter sized cubes.


  • #5
    FarmerGreen
    Registered Users, Registered Users 2 Posts: 1,134 ✭✭✭FarmerGreen


    thecatspjs wrote: »
    Is 0.27x10^-6 meters cubed the same as 0.27 cm cubed?
    Without the cubed,
    Is 0.27x10^-6 meters the same as 0.27 cm ?


  • #6
    Greenmachine
    Registered Users, Registered Users 2 Posts: 5,063 ✭✭✭Greenmachine


    Michael Collins wrote: »
    Yes,

    [latex] \displaystyle 0.27 \times 10^{-6} \cdot \hbox{m^3} [/latex]

    100 cm in every m, so

    [latex] \displaystyle 0.27 \times 10^{-6} \cdot (100 \; \hbox{cm})^3 [/latex]

    [latex] \displaystyle 0.27 \times 10^{-6} \cdot (100^3 \; \hbox{cm}^3) [/latex]

    [latex] \displaystyle 0.27 \times 10^{-6} \cdot 10^6 \; \hbox{cm}^3 [/latex]

    [latex] \displaystyle 0.27 \; \hbox{cm^3} [/latex]


    What? surely 0.27x10^-4 meters = 0.27 cm


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  • #7
    FarmerGreen
    Registered Users, Registered Users 2 Posts: 1,134 ✭✭✭FarmerGreen


    FarmerGreen wrote: »
    Without the cubed,
    Is 0.27x10^-6 meters the same as 0.27 cm ?

    The 0.27 thing.
    Is a millionth the same as a hundredth.
    Hugely confused Ted.


  • #8
    FISMA
    Closed Accounts Posts: 2,616 ✭✭✭FISMA


    FarmerGreen wrote: »
    Without the cubed,
    Is 0.27x10^-6 meters the same as 0.27 cm ?

    10^-6 is a "micro" - one millionth
    10^-2 is a "centi" - one hundreth

    So, the two cannot be equal.

    0.27x10^-6m = 0.00000027m = 0.000027cm
    Greenmachine wrote: »
    What? surely 0.27x10^-4 meters = 0.27 cm

    First break up the power
    0.27x10^-4 m = 0.27 x 10^-2 x 10^-2 m,

    Call the 10^-2 what it is - "centi" and replace one of the above

    0.27x10^-4 m = 0.27 x 10^-2 x 10^-2 m = 0.27 x 10^-2 centi*m

    So we have
    0.27x10^-4 m = 0.0027cm = 0.000027m = 0.27x10-2cm


  • #9
    FarmerGreen
    Registered Users, Registered Users 2 Posts: 1,134 ✭✭✭FarmerGreen


    Go on!
    Say it.
    Oops.


  • #10
    FISMA
    Closed Accounts Posts: 2,616 ✭✭✭FISMA


    FarmerGreen wrote: »
    Go on!
    Say it.
    Oops.

    I prefer d'Oh!

    I never did like powers or conversions, especially adding them - 8.7E-2 + 2.3E-5...


  • #11
    Greenmachine
    Registered Users, Registered Users 2 Posts: 5,063 ✭✭✭Greenmachine


    FISMA wrote: »
    I prefer d'Oh!

    I never did like powers or conversions, especially adding them - 8.7E-2 + 2.3E-5...

    I had to look at your post a few times to work through it. Was confused at the two answer till I realised you were solving two different problems.


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