A bit late to ask now, but I'm puzzled. I had to make some dil HCl from conc and being about 13 years away from a lab had to settle for gravimetry using the kitchen scales. At about 36%, conc HCl is about 10 molar. Diluting it 1/10 by weight makes it about 1 molar, by 1/100 makes it M/10. Maximum error of about 20% if you assume it has a specific gravity (well, we are talking normality, not molarity here) of 1.0. So how did you end up being out by a factor of 2?
Supplementary questions:
1)Are you just being old fashioned using normality, or is it still conventional in your parts?
2)How come you are diluting conc HCl to get N/10? Has your lab no molar HCl? I had to because the local lab suppliers wouldn't sell me any molar HCl in case I was making bombs (honest) but the pharmacy where I get my regular medicines was happy to sell me half a litre of conc.