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Math Help - A fathom is a method for measuring lengths, usually reserved for measuring the depth

  1. #1
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    A fathom is a method for measuring lengths, usually reserved for measuring the depth

    A fathom is a method for measuring lengths, usually reserved for measuring the depth of water. A fathom is approximately 6 ft in length . Take the distance to the moon to be 250 000 miles, and use the approximation above to find the distance in fathoms .


    I try to solve :

    I fa = 6 ft
    I mi = 5280 ft

    then : 250 000 X 5280
    = 132000000
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  2. #2
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    Quote Originally Posted by r-soy View Post
    A fathom is a method for measuring lengths, usually reserved for measuring the depth of water. A fathom is approximately 6 ft in length . Take the distance to the moon to be 250 000 miles, and use the approximation above to find the distance in fathoms .


    I try to solve :

    I fa = 6 ft
    I mi = 5280 ft

    then : 250 000 X 5280
    = 132000000
    Now divide that by 6 to get the number of fathoms.
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  3. #3
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    Quote Originally Posted by masters View Post
    Now divide that by 6 to get the number of fathoms.

    thanks
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  4. #4
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    Helolo, r-soy!

    I'll show you a neat way to convert units.


    A fathom is a measure, usually reserved for measuring the depth of water.
    A fathom is approximately 6 ft in length.
    Take the distance to the moon to be 250 000 miles,
    and use the approximation above to find the distance in fathoms.

    We know that: . \text{1 mile} \:=\:\text{5280 feet}
    Form a fraction with the two terms.
    . . There are two possible fractions: . \frac{\text{1 mile}}{\text{5280 feet}}\:\text{ and }\:\frac{\text{5280 feet}}{\text{1 mile}} .[1]


    We know that: . \text{1 fathom} \:=\:\text{6 feet}
    Form a fraction with the two terms.
    . . There are two possible fractions: . \frac{\text{1 fathom}}{\text{6 feet}}\:\text{ and }\:\frac{\text{6 feet}}{\text{1 fathom}} .[2]


    We want to convert 250,000 miles to fathoms.

    . . Begin with: . \frac{250,000\:\text{miles}}{1}


    Multiply by a fraction from [1].
    . . Select the fraction so that "miles" will cancel.

    . . \frac{250,\!000\:{\color{red}\rlap{/////}}\text{miles}}{1}\cdot\frac{\text{5280 feet}}{1\:{\color{red}\rlap{////}}\text{mile}} \;=\;1,\!320,\!000,\!000\text{ feet}


    Multiply by a fraction from [2].
    . . Select the fraction so that "feet" will cancel.

    . . \frac{1,\!320,\!000,\!000\:{\color{red}\rlap{///}}\text{feet}}{1} \cdot\frac{\text{1 fathom}}{6\:{\color{red}\rlap{///}}\text{feet}} \;=\; 220,\!000,\!000\text{ fathoms}


    ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~


    This, of course, can be done in one multiplication:

    . \frac{250,000\:{\color{red}\rlap{/////}}\text{miles}}{1} \cdot \frac{5280\:{\color{red}\rlap{///}}\text{feet}}{1\:{\color{red}\rlap{////}}\text{mile}} \cdot\frac{\text{1 fathom}}{6\:{\color{red}\rlap{///}}\text{feet}} \;=\;220,\!000,\!000\text{ fathoms}



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