sh script help with numeric values

[Ernie Luzar]

Hello list

I am having trouble getting leading zeros to show up.
The following is an example of what i mean.

   dirname="dir"
   dup_count=000
   dup_times=5

   while [ "${dup_count}" -ne "${dup_times}" ]; do
       dup_count=$(( $dup_count + 001 ))
       dname="${dirname}-${dup_count}"
       echo "${dname}"
   done

Outputs this
dir-1
dir-2
dir-3
dir-4
dir-5

What I really want to see is this
dir-001
dir-002
dir-003
dir-004
dir-005
dir-013
dir-111
ect

How do I get the leading zeros to show?

Thanks for your help