Significant Figures in 36 2/3

Date: 11/06/2001 at 15:58:11
From: E. S. Holzworth
Subject: Significant Figures

How many significant figures are there in the area "36 2/3 Acres"?

This type of notation for acreages is common in old deeds, yet with 
current standards in most jurisdictions in the U.S.A., areas and 
sub-areas are to be measured in acres to 4 decimal places (i.e. 
36.6667 Acres). Any calculations based on the deeded area figure 
should take significant figures into account. 

My conclusion: 36 2/3 = 36.67 decimal.

Date: 11/07/2001 at 08:39:39
From: Doctor Peterson
Subject: Re: Significant Figures

Hi, E.S.

Interesting question! My first thought was to apply what I said here:

   Fraction or Decimal?
   http://mathforum.org/library/drmath/view/58148.html   

To a mathematician, a fraction represents an exact number - 
effectively, infinitely many decimal places. A decimal number might 
represent an approximation, whose precision is implied by the number 
of significant digits.

But it's also possible to take a fraction as a rough number: 
"about 2/3." In that case, you can estimate its precision by thinking 
of it as a quotient; since the numerator and denominator each have one 
significant digit, it could be taken as having one significant digit, 
so we would take it as 0.7. Since in addition it is not the number of 
significant digits, but the number of decimal places that counts, and 
since the whole part of a mixed number can be seen as a precise number 
(constrained as it is to be a whole number), your number would then be 
36.7, with three effective significant digits and one decimal place.

But legally, I would think the real issue would be to determine the 
intent of the original deed, rather than to legalistically count 
digits in the number as written. I doubt that precision was even 
considered when it was written; so the only reasonable thing I can see 
to do is to take it at face value as an exact number, and then rewrite 
it according to modern standards as 36.6667 rounded to four decimal 
places. Other considerations might have to be taken into account, such 
as the accuracy of measurements used to calculated that figure, but I 
can't see any better answer given what you have told me. Is there any 
law dictating how to interpret old deeds?

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