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Math Help - Quantity and Symbolic representations

  1. #1
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    Smile Quantity and Symbolic representations

    The Sahara Desert covers about 8.3x10^13 sqaure feet.

    The average depth of the sand in the Sahara Desert is 200 feet.

    A grain of sand has a volume of approx. 1.3 x 10^-9 cubic feet.

    Which of the following is the best estimate of the number of grains of sand in the Sahara Desert?

    A. 10^22
    B. 10^23
    C. 10^24
    D. 10^25

    Can anyone let me know how to go about solving this problem? I know these are in scientific notation, but I have no idea how they get to these answers.

    Does anyone know the answer?
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  2. #2
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    Quote Originally Posted by LisaMedrano View Post
    The Sahara Desert covers about 8.3x10^13 sqaure feet.

    The average depth of the sand in the Sahara Desert is 200 feet.

    A grain of sand has a volume of approx. 1.3 x 10^-9 cubic feet.

    Which of the following is the best estimate of the number of grains of sand in the Sahara Desert?

    A. 10^22
    B. 10^23
    C. 10^24
    D. 10^25

    Can anyone let me know how to go about solving this problem? I know these are in scientific notation, but I have no idea how they get to these answers.

    Does anyone know the answer?
    Do you understand the scientific notation?

    Think about the problem a little. You want the volume of the sand in the desert first, so to do that you multiply the area by the depth. To get the number of grains of sand you divide the volume of sand by the volume of each grain. so (8*10^13 * 200)/1.3*10^9 is about 1.28*10^25, D.
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  3. #3
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    Quote Originally Posted by JeWiSh View Post
    Do you understand the scientific notation?

    Think about the problem a little. You want the volume of the sand in the desert first, so to do that you multiply the area by the depth. To get the number of grains of sand you divide the volume of sand by the volume of each grain. so (8*10^13 * 200)/1.3*10^9 is about 1.28*10^25, D.
    I honestly can't think back on how to divide when using scientific notation. Do I add the exponents? Is there a way you could type out the process.

    Thanks!

    Sincerely,

    Mathematically Challenged.
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  4. #4
    Like a stone-audioslave ADARSH's Avatar
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    Quote Originally Posted by LisaMedrano View Post
    I honestly can't think back on how to divide when using scientific notation. Do I add the exponents? Is there a way you could type out the process.

    Thanks!

    Sincerely,

    Mathematically Challenged.

    Try remembering this for ever


    <br />
\frac{a^x}{a^{y}} = a^{x}\times a^{-y} = a^{x-y}

    Quote Originally Posted by LisaMedrano View Post
    The Sahara Desert covers about 8.3x10^13 sqaure feet.

    The average depth of the sand in the Sahara Desert is 200 feet.

    A grain of sand has a volume of approx. 1.3 x 10^-9 cubic feet.

    Which of the following is the best estimate of the number of grains of sand in the Sahara Desert?

    A. 10^22
    B. 10^23
    C. 10^24
    D. 10^25

    Can anyone let me know how to go about solving this problem? I know these are in scientific notation, but I have no idea how they get to these answers.

    Does anyone know the answer?
    Total area of Sahara Desert

    = 8.3\times 10^{13}sq.feet

    Depth of Sahara desert

    =200 feet

    Volume of the desert =

     depth\times area=8.3\times 2\times 10^{2+13}= 16.6\times 10^{15}cubic~feet


    Note: In the above step 200 x 10^(13) = 2x10^(2) x 10^(13) = 2 x 10^(2+13)



    Volume of a single grain
    = 1.3 \times 10^{-9} cubic ~feet


    So total number of grains = \frac{volume~of~Desert}{volume~of~a~grain}

    = \frac{16.6\times 10^{15}}{ 1.3 \times 10^{-9} }

    = \frac{1.66\times 10^{16}}{ 1.3 \times 10^{-9} }

    = \frac{1.66\times 10^{16}}{ 1.3 \times 10^{-9} }

    1.66/1.33 is approximately taken 1 considering the options

    thus Answer is


    = \frac{ 10^{16}}{ 10^{-9} }

    =  10^{16-(-9)}

    = 10^{16+9}=10^{25}
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  5. #5
    MHF Contributor

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    I would have started approximating from the start:
    8.3 x 10^{13}\approx 10^{14} since 8> 5
    200\approx 10^2
    1.3 x 10^{-9}\approx 10^{-9}

    10^{14}10^2/10^-9= 10^{14+2+ 9}= 10^{25}
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