Do the quotient always have the same number of digits when dividing 3 digit numbers by 1 digit number

This statement is false because if a three-digit number such as 121 were divided by 7, you would get 17.2857143. That is a two digit number.
This is just one example of why that statement is false and there are many more examples, but just this one can prove it wrong.

Hope I helped and good luck!