Filter a range of values my cell values fall into

I am working with 2 worksheet in the same workbook. Sheet1 has the values. Sheet 2 has the table of data with header. My goal is to read the values from sheet1 and then filter a specific column with that said value. I can get that far. The issue is my value in sheet1 is not an exact value of what would be in sheet2. for example. In sheet1 I have values of a = 5.68. Now when I go in sheet2 it does not have 5.68 in the "a" column but I want to select and filter the values that a =5.68 falls into. for example sheet2 may have 4.5 and 7.5. if those are the values closest/nearest to the a values then I want to filter them. In summary if a = 5.68 in sheet 2, then I go in sheet2 and filter the range that 5.68 falls into and those values would be 4.5 and 7.5 and take the resulting value in the next column and paste it in a new sheet.

Update:

I have to filter those values in that column... in column A... row 2 (A2) may be 4.5 and row 20 (A20) may be 7.5..but those are the values that 4.5 fall within. Because filtering those values will results in another set of values in column B. Then I also have a b value that I will filter the range for in column. I would do that process 3 times with 3 values (a,b,c) from sheet1 and filter the range they fall into in sheet2 in column (A,B,C) to get a final values in Column D.....

Here's what I started with:

 Sub Filter_criteria()
 Dim A As String

 With Worksheets("Sheet1")
  Set Al = .Range("A11")
 End With
 With Worksheets("Sheet2")
  With .Range("A1:N"& Cells(.Rows.Count, "N").End(xlUp).Row)
   .AutoFilter
   Range("K1").AutoFilter Field:=11, Criteria1:=A, Operator:=xlFilterValues
  End With
  .AutoFilterMode = False
 End With
 End Sub