9-லிருந்து அனைத்தும், 10-லிருந்து கடைசி
All From 9, Last From 10
The fastest way to subtract from 1000, 10000, or any power of ten. Learn the Nikhilam sutra that turns hard subtraction into a 3-second exercise.
Let's Learn
What you will learn today
Subtract any number from 1000, 10000, or any power of ten using the Nikhilam sutra in seconds.
What is a complement of 10?
Quick: what do you add to 4 to get 10? To 7? To 3? (6, 3, 7.) If you can answer these instantly, the core of today's lesson is already in your head.
Today's sutra: 'Nikhilam Navatascaramam Dasatah' — which means 'All from 9 and the last from 10.' It sounds like poetry, but it is a precise instruction: subtract each digit from 9, except the last digit, which you subtract from 10. That's it. You can now do 1000 − 647 in your head.
நிகிலம் நவதஸ்சரமம் தஸதஹ — 9-லிருந்து அனைத்தும், 10-லிருந்து கடைசி.
The rule, step by step
To subtract a number from a power of 10 (100, 1000, 10000...):
- Take each digit of the number you are subtracting
- Subtract each digit from 9 — EXCEPT the last digit
- Subtract the last digit from 10
- The result is your answer
📐 Example: 1000 − 347
We subtract 347 from 1000. Digits: 3, 4, 7.
- 19 − 3 = 6
- 29 − 4 = 5
- 310 − 7 = 3 (last digit: subtract from 10, not 9)
- 4Answer: 653. Check: 653 + 347 = 1000 ✓
📐 Example: 10000 − 4382
Four-digit number, subtract from 10000:
- 19 − 4 = 5
- 29 − 3 = 6
- 39 − 8 = 1
- 410 − 2 = 8 (last digit from 10)
- 5Answer: 5618. Check: 5618 + 4382 = 10000 ✓
Why does this work?
This is not a trick — it is the definition of a 10s-complement. When you subtract N from 1000, you are finding the number that adds to N to make 1000. That number is exactly what 'all from 9, last from 10' computes: it gives you each digit of the 10s-complement position by position.
What about trailing zeros?
1000 − 400: digit is just 4, but we have three decimal positions. Treat 400 as 400: digits 4, 0, 0. Apply rule: 9−4=5, 9−0=9, 10−0=10 — but 10 makes the tens digit... Actually: for trailing zeros, keep them as zeros and the rule still works: 600. Better: recognise 1000−400 = 600 directly. The sutra works best for non-zero last digits.
கடைசி இலக்கம் பூஜ்ஜியமாக இருந்தால் — நேரடியாக கணக்கிடு.
Forgetting which digit to subtract from 10
Every digit is subtracted from 9 — except the LAST (rightmost) digit, which is subtracted from 10. Students often subtract all digits from 9. Check: if the last digit is 7, it becomes 10−7=3 (not 9−7=2).
Challenge Round
Challenge: 10000 − 6391
Apply the rule to this 4-digit subtraction. What are the four steps? What is the answer?
Nikhilam sutra: 'All from 9, last from 10' subtracts any number from a power of 10 in one pass. Each digit gets subtracted from 9, except the last which is subtracted from 10.
↪ Next: Multiplying by 11 — the elegant gap trick.
Key Points
முக்கிய குறிப்புகள்
- ✓Sutra: 'All from 9, last from 10' (Nikhilam)
- ✓Subtract each digit from 9, except the last digit which is subtracted from 10
- ✓Works for any subtraction from 100, 1000, 10000, etc.
- ✓This computes the 10s-complement digit by digit
Glossary
சொல் அகராதி
Nikhilam
நிகிலம்
Power of ten
பத்தின் அடுக்கு
Digit
இலக்கம்
10s-complement
10 நிரப்பு
Practice Activities
Quizவினாடி வினா
Answer each question to check your understanding.
Using 'All from 9, last from 10', what is 1000 − 273?
Fill in the Blanksஇடைவெளி நிரப்புக
Type the missing word and press Check or Enter.
Type the missing word and click Check.