...and wiggles decimal

Consider the following wiggle expression :

${\displaystyle 5_{10}{3}_{10}5{;}_{10}{4}_{10}9}$

Telescoping from the left and right,

${\displaystyle 5\times 10 = 50,}$

${\displaystyle 50+3 = 53,}$

${\displaystyle 53\times 10 = 530,}$

${\displaystyle 530+5; = 535;}$

and

${\displaystyle 9÷10=\frac{9}{10} (= 0.9),}$

${\displaystyle \frac{9}{10}+4 = 4\frac{9}{10} (= 0.9+4 = 4.9),}$

${\displaystyle 4\frac{9}{10} ÷10 = \frac{49}{100} = 4.9÷10 = 0.49,}$


so that, adding, and using the decimal form of the fraction, we get

${\displaystyle 5_{10}{3}_{10}5{;}_{10}{4}_{10}9 = 535.49.}$

The wiggle form on the left closely corresponds to the decimal form on the right.  The superdigits on the left are exactly the digits on the right.  The face value marker on the left corresponds to the decimal point on the right.  The interbases on the left are all explicitly ${\displaystyle 10}$.  The number on the right is implicitly in our usual decimal or base ten notation.