Wiggle on the far side.

Recapping, my baby son's weight at his birth yesterday morning was, in ounces,

`\qquad\qquad\qquad 7_{16}12  =  124.`

Late this afternon, he weighed in at


`\qquad\qquad\qquad 7_{16}8  =  120.`

But what if I wanted pounds, rather than ounces?  This is easily done, but needs more notation and more thinking.

In both of the preceding wiggle expressions, the last superdigit---the 12 and the 8---appear at face value.  We were looking for an answer in ounces, and they represented numbers of ounces.  The 7, on the other hand, represented pounds, and so in ounces it was worth 16 times its face value.

With wiggle notation as we have learned it so far, the rightmost superdigit always appears at face value.

Now, we introduce the unit marker.  It is a semicolon, placed just to the right of the superdigit that we want to mark as being at face value.  Placing a semicolon immediately after the rightmost superdigit gives the same result as leaving it out :

`\qquad\qquad\qquad 7_{16}12;  =  7_{16}12  =  (7 xx 16)  +  12  =  124.`

`\qquad\qquad\qquad 7_{16}8;  =  7_{16}8  =  (7 xx 16)  +  8  =  120.`

To work in pounds instead of ounces, we move the semicolon to the 7, so that


`\qquad\qquad\qquad 7;_{16}12  =  7  +  (16 \\ 12)  =  7\frac{12}{16}  =  7\frac{3}{4}.`

`\qquad\qquad\qquad 7;_{16}8  =  7  +  (16 \\ 8)  =  7\frac{8}{16}  =  7\frac{1}{2}.`

My boy was `7\frac{3}{4}` pounds at birth, but is down to `7\frac{1}{2}` pounds today.  (Those are the actual weights I was given.  I haven't fudged them for pedagogical advantage.)

There needs to be a better handle on the use of the semicolon, and as shall soon be seen, there is.