To find the multiplicative inverse, convert the number to a fraction and flip it over.
First, note that
Next, remember that the multiplicative inverse of any nonzero number is the number whose product with the original number is
So, if we want the multiplicative inverse of
#=1/(1/10) xx 10/10#
(multiplying the numerator and denominator by the same number doesn't change our value)
So the multiplicative inverse of
As a side note, it's a useful trick to remember that