Millimeters, Inches, Feet, Miles

Date: 07/10/2003 at 19:23:10
From: Erik
Subject: Metric to English/British conversion

The question is rather elementary, but one for which I haven't found 
a satisfactory answer. The conversions given for millimeters to inches 
is 25.4, and for feet to miles is 5280. Are these numbers exact? Are 
there exactly 160934400 millimeters in 100 miles?

Date: 07/10/2003 at 22:48:40
From: Doctor Peterson
Subject: Re: Metric to English/British conversion

Hi, Erik.

Surprisingly, these two conversions are both exact. For details on 
the current definition of the inch, see

  A Tale of Two Feet OR The Case of The Double Standard - T. J. Keefe
  http://physics.ccri.cc.ri.us/keefe/twofeet.htm 

  The US Metric Law of 1866 said that one meter was equal to 39.37
  inches, exactly. In 1959, the relationship between inches and
  centimeters was redefined to be that one inch is equal to 2.54
  centimeters, exactly. Maps produced by the US Coast and Geodetic
  Survey continued to use the old standard. To clarify which foot
  you are talking about, the old foot, derived from 1 meter = 39.37
  inches (exactly), is referred to as the "US survey foot". The new
  foot, derived from 1 inch = 2.54 cm (exactly), is referred to as
  the "international foot".

Of course, this is the American definition; I don't know whether the 
British inch is defined the same way.

See also

  Inch - Eric Weisstein's World of Physics
  http://scienceworld.wolfram.com/physics/Inch.html 

  An nonmetric unit of length, originally defined as the lengths of
  three "average size" barleycorns laid end-to-end, but now more
  rationally defined as 2.54 cm. An older definition no longer used
  was 1 meter = 39.37 inches, giving 2.54000508 cm/inch. 

The number of feet in a mile has always been a whole number, though 
not always the same one. According to

  How Many? A Dictionary of Units of Measurement - Russ Rowlett
  http://www.unc.edu/~rowlett/units/ 

  The word comes from the Latin word for 1000, mille, because
  originally a mile was the distance a Roman legion could march in
  1000 paces (or 2000 steps, a pace being the distance between
  successive falls of the same foot). There is some uncertainty
  about the length of the Roman mile. Based on the Roman foot of
  29.6 centimeters and assuming a standard pace of 5 Roman feet,
  the Roman mile would have been 1480 meters (4856 feet); however,
  the measured distance between surviving milestones of Roman roads
  is often closer to 1520 meters or 5000 feet. In any case, miles
  of similar lengths were used throughout Western Europe. In
  medieval Britain, several mile units were used, including a mile
  of 5000 feet (1524 meters), the modern mile defined as 8 furlongs
  (1609 meters), and a longer mile similar to the French mille
  (1949 meters), plus the Scottish mile (1814 meters) and the Irish
  mile (2048 meters). In 1592 the British Parliament settled the
  question by defining the statute mile to be 8 furlongs, 80
  chains, 320 rods, 1760 yards or 5280 feet. The statute mile is
  exactly 1609.344 meters. 

If you have any further questions, feel free to write back.

- Doctor Peterson, The Math Forum
  http://mathforum.org/dr.math/