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 compared to 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 into un-normalize solution. Please advice if you realize I miss out several important points.

Thanks
Yan Cheng CHEOK