The Sutra means “All from 9 and the last from 10”. In mathematical terms, this means find complement of a number. Subtract the number from the nearest power of 10 such as 10, 100, 1000 etc. The power of 10 from which the difference is calculated is called the Base.
The difference between the number and the base is termed as deviation or reference base or complement which may be positive or negative.
Example:
| Number | Base | Base – Number | Complement / Nikhilam |
| 7 | 10 | 7 – 10 | -3 |
| 14 | 10 | 14 – 10 | 4 |
| 88 | 100 | 88 – 100 | -122 |
| 109 | 100 | 109 – 100 | 9 |
| 5200 | 10000 | 5200 – 10000 | -4800 |
Exercise:
1) Find the compliment and the nearest base of the following numbers
a) 45
b) 8
c) 13
d) 8910
e) 98
f) 105
g) 989
h) 99999
i) 1000001
Mathsbaron 