Partial Product Division and Decimals don't mix

A typical Partial Product Division problem would look like this:
172 / 5
Can you take 5 x 100 out? (500) No, too big.
Can you take 5 x 10 out (50) Yes.  How many of these could you take out? At least 3.  Ok, so 5 x 30 = 150.
172 - 150 = 22
Can we take out any more 5 x 10? (50) No.
Can we take out 5 x 5? (25) No.
Can we take out 5? Yes.  How many 5s could we take out?  At least 4.  5 x 4 = 20.
22 - 20 = 2.  Can we take another 5 out? No.  So let's add up our answer:
30 + 4 = 34; so the answer is 34 with remainder 2.  Actually, when we do it, we tend to take out each 10, and then each number after that.  So, we would've done 10 + 10 + 10 + 4 and remainder 2.  Anyhow.
This is much trickier when you introduce The Decimal (dun dun DUN). 
Same problem with a twist:
17.2 / 5
Can we take out a 5 x 10? (50) No.  But we could take out 5 x 1.0, and we could do this 3 times:)
5 x 3.0 = 15.0.  17.2 - 15.0 = 2.2
Can we take out a .5? (2.5) No.
Can we take out a .1? (.5) yes.  We can take out about 4 .1s, or 5 x .4 = 2.0.
2.2 - 2.0 = 0.2  So our remainder is 0.2
Let's add (the fun part - dun dun DUN)
3.0 + 0.4 = 3.4 with a remainder of 0.2
But now try it by taking out each part individually (make sure you line up all those decimals correctly!):
1.0 + 1.0 + 1.0 + 0.1 + 0.1 + 0.1 + 0.1
OR, try it with a much larger number:
172.54 / 59
Yiiiiiiikes!!!!
But the good news is, it is a really good mental exercise in Place Value.