Solution
- 
Define a range to use as the lookup value
 
- 
Create the dropdown list
 
- 
Paste in some code
 
Step 1: Setup Sheet2 like this and define a Named Range as _descrLookup:

( Highlight -> Right-Click -> "Define Name..." )
This is an optional step, but it just makes it easy to follow for Step 3.
Step 2: In Sheet1, create the dropdown using Data Validation and use the VALUES YOU WANT TO BE SHOWN IN THE DROPDOWN as the source. In this example it's Sheet2 A2:A4 (see above image):

( Data -> Data Validation )
Step 3: Add some VBA code to Sheet1:
( Right-Click the tab Sheet1 -> View Code )
Paste this into the code window for Sheet1:
Private Sub Worksheet_Change(ByVal Target As Range)
    selectedVal = Target.Value
    If Target.Column = 4 Then
        selectedNum = Application.VLookup(selectedVal, Worksheets("Sheet2").Range("_descrLookup"), 2, False)
        If Not IsError(selectedNum) Then
            Target.Value = selectedNum
        End If
    End If
End Sub