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

Oct 2009
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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
 

masters

MHF Helper
Jan 2008
2,550
1,187
Big Stone Gap, Virginia
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.
 

Soroban

MHF Hall of Honor
May 2006
12,028
6,341
Lexington, MA (USA)
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: .\(\displaystyle \text{1 mile} \:=\:\text{5280 feet}\)
Form a fraction with the two terms.
. . There are two possible fractions: .\(\displaystyle \frac{\text{1 mile}}{\text{5280 feet}}\:\text{ and }\:\frac{\text{5280 feet}}{\text{1 mile}}\) .[1]


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


We want to convert 250,000 miles to fathoms.

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


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

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


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

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


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

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