$```$

def multiply$($s$)$:

$"""($str$)->$ str

Takes as input a string s representing an expression consisting of a product of numbers.

Returns a string representing the product in scientific notation with the correct

number of significant digits, according to the rule of thumb for multiplication

with significant digits.

$>>>$ multiply$("1*9\mathrm{.}9")$

$\text{'}1.$e$1\text{'}$

$>>>$ multiply$("10.*9\mathrm{.}95")$

$\text{'}1\mathrm{.}0$e$2\text{'}$

$>>>$ multiply$("2\mathrm{.}999999*999")$

$\text{'}3\mathrm{.}00$e$3\text{'}$

$>>>$ multiply$("500*2\mathrm{.}00")$

$\text{'}1.$e$3\text{'}$

$>>>$ multiply$("500.*2\mathrm{.}00")$

$\text{'}1\mathrm{.}00$e$3\text{'}$

$>>>$ multiply$("000\mathrm{.}0012*2\mathrm{.}000001")$

$\text{'}2\mathrm{.}4$e$-3\text{'}$

$>>$ multiply$(\text{'}\mathrm{.}002*\mathrm{.}004*1\mathrm{.}2\text{'})$

$\text{'}1.$e$-5\text{'}$

$>>>$ multiply$(\text{'}\mathrm{.}2*\mathrm{.}4*1\mathrm{.}2\text{'})$

$\text{'}1.$e$-1\text{'}$

$>>>$ multiply$(\text{'}3\mathrm{.}002*\mathrm{.}004*1\mathrm{.}2\text{'})$

$\text{'}1.$e$-2\text{'}$

$>>>$ multiply$(\text{'}3\mathrm{.}002*\mathrm{.}0040*1\mathrm{.}20000\text{'})$

$\text{'}1\mathrm{.}4$e$-2\text{'}$

$>>>$ multiply$(\text{'}3\mathrm{.}002*\mathrm{.}004000*1\mathrm{.}20000\text{'})$

$\text{'}1\mathrm{.}441$e$-2\text{'}$

$>>>$ multiply$("000\mathrm{.}0012*2\mathrm{.}000001")$

$\text{'}2\mathrm{.}4$e$-3\text{'}$

$>>>$ multiply$("000\mathrm{.}0012*2\mathrm{.}000001*1\mathrm{.}00007*1000.")$

$\text{'}2\mathrm{.}4$e$0\text{'}$

$>>>$ multiply$("11*12*10")$

$\text{'}1.$e$3\text{'}$

$```$