Vedic Sutra #2:     All from 9 and the last from 10

We want to subtract a number from a power of 10, like 100 or 1000 or 10,000 etc..
Example: 10000 - 4782 = ?

  1. We subtract each digit from 9 except the last.
    That's the "All from 9 and the last from 10".
  2. That gives: 9 - 4 = 5, 9 - 7 = 2, 9 - 8 = 1
  3. That gives 521X
  4. We subtract the last digit from 10, and, since 10 - 2 = 8, the answer is 5218

Why?
10000 - 4782 = 5218 is correct if 10000 = 4782 + 5218 and
(starting the addition from the right)
2 + 8 = 10 and that "1" carries to the left,
turning all the 9s into 10s
... and the "1" carries on ... and on ...