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Math Help - Quick Conversion question

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    Quick Conversion question

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    qbkr21

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    Quote Originally Posted by qbkr21 View Post
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    qbkr21

    1 \text{ Angstom} = 1.0 \times 10^{-10} \text{ meters} and 1 \text{ meter} = 1.0 \times 10^9 \text{ nanometers}

    thus

    1.4 {\color{red}\text{ Angstoms}} = 1.4 (\underbrace{{\color{red}1.0 \times 10^{-10} \text{ meters}}}_{\text{this replaces Angstoms}}) = 1.4 \times 1.0 \times 10^{-10} \times (\underbrace{{\color{red}1.0 \times 10^9 \text{ nanometers}}}_{\text{this replaces meters}})

    we just keep replacing the units with their equivalents

    or, to do it your way:

    1.4 \text{ Angstom} \times \frac {10^{-10} \text{ meters}}{1 \text{ Angstom}} \times \frac {10^9 \text{nanometers}}{1 \text{ meter}}
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    RE:

    RE:

    Where did I go wrong doing it my way? I'd like to figure out how the exponents in Scientific Notation correlate to the problem. If the sign changes if goes on top or bottom. Can you help me with this?

    qbkr21
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    RE:

    What if we were given meters and told to turn them into Angstroms; would the 1.0 X 10^-10 become 1.0 X 10^10 since it would be put on the bottom?
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    RE:

    RE:

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    Quote Originally Posted by qbkr21 View Post
    RE:

    Where did I go wrong doing it my way? I'd like to figure out how the exponents in Scientific Notation correlate to the problem. If the sign changes if goes on top or bottom. Can you help me with this?

    qbkr21
    to take something from the top and put it in the bottom, or vice versa, we change all the exponents to their negatives. but that is not necessary here. in the denominator we only have 1's. so we just multiply all the numerators together.

    to answer your first question: yes, the negative sign stays on top. it is not necessary to move it to the bottom, so don't worry about it. moving it to the bottom will mess you up
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    Quote Originally Posted by qbkr21 View Post
    RE:

    i gave you the conversion. 1 meter is 10^9 nanometers. you had that wrong. your exponent should be 9 not -9. a nanometer is smaller than a meter
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    RE:

    RE:

    So would

    1 Meter = 1 X 10^2 centimeters?
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    Quote Originally Posted by qbkr21 View Post
    RE:

    So would

    1 Meter = 1 X 10^2 centimeters?
    yes. 1 meter is 100 centimeters
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    RE:

    Jhevon for some reason I have all of my units mixed up. Maybe you can help. Here are the units that I was given, can you correct them so that I can avoid future error?

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    Quote Originally Posted by qbkr21 View Post
    Jhevon for some reason I have all of my units mixed up. Maybe you can help. Here are the units that I was given, can you correct them so that I can avoid future error?

    this has meters on the right and (prefix)meters on the left. this table is correct. in what we did, the coefficient of meter was 1. that is not the case in this table. you have to solve for 1 meter to do our problem

    example: the table says,

    1 \text{ nanometer} = 1 \times 10^{-9} \text{ meters}

    this is correct, but we want 1 meter = something nanometers. multiply both sides by 10^9 to obtain

    1 \times 10^9 \text{ nanometers} = 1 \times 10^{-9} \times 10^9 \text{ meters} = 1 \times \times 10^{-9 + 9} \text{ meters} = 1 \text{ meter}
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    RE:

    When we convert do we usually try and get meters by itself?
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    RE:

    RE:

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    Quote Originally Posted by qbkr21 View Post
    When we convert do we usually try and get meters by itself?
    not always. in this problem it was convenient though

    we avoided having anything in the denominator that we would otherwise have
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    Quote Originally Posted by qbkr21 View Post
    RE:

    yes, that is good

    or you can write it as 1 \text{ meter} = 1 \times 10^{-15} \text{ petameter}
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