Henry I. answered 03/14/19
Experienced, Patient Math and English teacher
Assuming the original amount is $100, then a 10% profit would be $10. To obtain that $10 figure (plus the original $100), you would multiply by 1.1, as you suggested. Note that dividing by 0.9 would give you a different (and incorrect) answer of 1.11111...
There are other ways to prove this answer, but my technique, which I recommend highly, was simply to substitute simple numbers into your problem and analyze from there.
Best wishes