Precision of number not maintained when saved via Export

Question

Assume that the output of my calculation is a and is a number such as:

a = 100.1252135246354847;

N[a] gives me 100.125

However, when I try to save my data, a via export such as :

Export["/path/to/file/with/extension/dat", N[a]]

My eventual filename.dat has 100.12521352463548 and not 100.125. So is the precision of digits/most significant digits for display only?

I also tried NumberForm[a,6] and I get NumberForm[100.1252135246354847`18.000543455259304, 6] in my data file!

What am I doing wrong?

Edit (possible solution):

Replacing N[a] with SetPrecision[a,5] helped. I wasn't sure if I should have this in the ANSWER section because the solution may be quite trivial and may not warrant being in the answer section. Any thoughts on that (whether or not I should answer this question or let the solution remain as an appended "edit")

Answer 1

Put the path between the quotation marks.

a = 100.1252135246354847;  
Export[StringJoin["", ToString[N[a, 6]], ".dat"], a]  

100.125.dat

Answer 2

Replacing N[a] with SetPrecision[a,5] helped. The above answer by Fred Daniel Kline helps too but isn't really what I am looking for.