Sneaky subtractions

Here's a way of doing subtraction calculations that is rather sneaky. As long as you can do addition this is a cinch.

Example 1: find 4673 – 2198.
Method:
(a) Write down what you need to make each digit in the second number up to 9: i.e. 7801.
(b) Add this to the first number:
   4673
+ 7801
 12474
(c) Delete the 1 at the front of this and add it to the final digit: 2475.
That's the answer!

Make sure the two numbers have the same number of digits, by putting in leading zeros if necessary:

Example 2: find 5018 – 846.
Rewrite this as 5018 – 0846. Then using the method above ...

   5018 – 0846
+ 9153
 14171 giving the answer 4172 (by deleting the 1 at the front of 14171 and adding it to the final digit.)

It works with decimals as well!

Example 3: find 6.254 – 0.98.
Rewrite this as 6.254 – 0.980

   6.254 – 0.980
+ 9.019
 15.273 giving the answer 5.274 (by deleting the 1 at the front of 15.273 and adding it to the final digit.)

Try it! It really works.
But can you explain why??