Friday, January 22, 2010

How many pounds? How many ounces? --part 1.

My new littlest, a boy, was born yesterday.  He weighed 7 lb., 12 oz.  If I let his birthweight be w, then

            w= lb. +12 oz.

Apposition is the writing of one thing beside another.  In my youngest son's birthweight, 7 lb. and 12 oz. are apposed, and this means they should be added.  Similarly, in a mixed fraction such as 7¾, the 7 is apposed to the ¾, and that, too, means that they should be added.  Notice that this well-established convention conflicts somewhat with the usual algebraic convention that when one thing is put beside another, they should be not added but multiplied, i.e.

7a=7×a.

There is a formal rule for avoiding conflicts between these two different meanings of apposition: 
  • Quantities with different units are to be added if they are separated by a comma and a space.
  • A whole number and a fraction are to be added if the number comes before the fraction and there is no space between them.  
  • Quantities are to be multiplied, as in algebra, if they are separated simply by a space.

Now that we have dealt with these conventions, let's write my youngest son's birthweight in a a variety of ways:

            w=7 lb., 12 oz. =124 oz. =734 lb.

The first of these keeps the numbers small, but uses two different units.  The second uses just one unit, at the price of a larger number.  The third also uses just one unit, at the price of employing a fraction.

No comments:

Post a Comment