using LEFT, MID, RIGHT with INDEX, MATCH?

Hello -

I'm trying to do something for work but I'm not sure I'm going about it the right way. If I am, I feel like I'm close. Here's what I'm trying to do. I want to have a hidden table (one column with letters, one column with numbers), and I want to return all of the corresponding letters when a user enters a number value.

For example, in the attached spreadsheet, I entered my table in A1:B10. In cell A13 I am just combining INDEX and MATCH functions to return the value. The argument I plugged in was 7. I want that to be a variable that is pulled from what the user enters.

In cell A16, I have 13.69. This is where the user will enter the numeric value, and I want my formula to return all alpha characters based on the table. Below that I'm testing out LEN, LEFT, MID, RIGHT. It seems LEN returns a numeric value and therefore my formula in C19 works. LEFT, MID, and RIGHT, however, seem to return a text value and then my formula does not work.

Am I going about this wrong? Is there a fix to this or possibly a better way of tackling this problem? Thanks much!