Shall I apply normalization in the following case?

For example, for the following table,


measurement (without normalization)
===========
id | value | measurement_unit | measurement_type
------------------------------------------------
1   0.23     mm                    width
2   0.38     mm                    width
2   0.72     mm                    width


If I normalize to the following format, I will encounter several problem compared to table without normalization



measurement (normalization)
===========
id | value | measurement_unit_id | measurement_type_id
------------------------------------------------------
1   0.23     1                    1
2   0.38     1                    1
2   0.72     1                    1


measurement_unit_id
===================
id | value
----------
1  | mm


measurement_type_id
===================
id | value
----------
1  | width


(1) When rows grow to few millions in table measurement, the join operation on normalization table, is *much* slower
comparedto non-normalization table.  

One of the most frequent used query, To retrieve "value", "measurement_unit" and "measurement_type",  I need to join
measurement+ measurement_unit_id + measurement_type_id. 

For non-normalization table, I need NOT to join.

Right now, I cannot justify why I need to use normalization. I afraid I miss out several important points when I turn
intoun-normalize solution. Please advice if you realize I miss out several important points. 

Thanks
Yan Cheng CHEOK