\newcommand{\exponentColor}[1]{\color{purple}{#1}}\newcommand{\leadingColor}[1]{\color{green}{#1}}
Express this number in scientific notation.
PRETTY_DECIMAL
\times 10
E
There are \exponentColor{E} digits to the right of the leading \leadingColor{LEADING} (and to the left of the decimal).
Count the zeroes to the right of the decimal point before the leading \leadingColor{LEADING}: there is 1 zeroare (E + 1) * -1 zeroes.
If you count the leading digit \leadingColor{LEADING} and those zeroes and the 1 zero, there is \exponentColor{E * -1} digit to the right of the decimal point.
If you count the leading digit \leadingColor{LEADING} and those zeroes and the 1 zero, there are \exponentColor{E * -1} digits to the right of the decimal point.
So: PRETTY_DECIMAL = \leadingColor{LEADING}TRAIL \times 10^{\exponentColor{E}}
SCIENTIFIC = {?}
DECIMAL
SCIENTIFIC = BASE_STR \times TEN_POWER
BASE_STR \times TEN_POWER = PRETTY_DECIMAL