100-க்கு அருகில் உள்ள எண்களை பெருக்கல்
Multiply Numbers Near 100
98 × 97 = 9506. Solved in two mental steps. The same principle that worked for numbers near 10 now scales to hundreds — and the answers are just as elegant.
Let's Learn
What you will learn today
Apply the Nikhilam base method to numbers near 100, including numbers above 100.
Recap: base-10 Nikhilam
You learned: deficiency from 10 → cross (one number minus the other's deficiency) → units (product of deficiencies). Now the same idea, but deficiencies are from 100.
98 × 97 looks frightening. But with the base-100 method, it becomes: deficiencies 2 and 3, cross: 98−3=95, units: 2×3=06. Answer: 9506. Three mental steps for a multiplication that most people can't even attempt in their head.
100-க்கு அருகில் உள்ள எண்கள் — அதே விதி, பெரிய எண்கள்.
The key difference from base-10
When the base is 100, the units part must be a 2-digit number (because 100 has two zeros). If the product of deficiencies is a single digit, pad it with a leading zero.
- Base 10: units part is 1 digit
- Base 100: units part is ALWAYS 2 digits (pad with 0 if needed)
- Example: deficiencies 2 and 3 → product=6 → write as 06, not 6
📐 Example: 98 × 97
Deficiency of 98: 2. Deficiency of 97: 3.
- 1Cross: 98 − 3 = 95 (or 97 − 2 = 95)
- 2Units: 2 × 3 = 6 → as 2-digit: 06
- 3Combine: 95 | 06 = 9506
- 498 × 97 = 9506 ✓
📐 Example: 96 × 94
Deficiencies: 4 and 6.
- 1Cross: 96 − 6 = 90
- 2Units: 4 × 6 = 24 (already 2 digits)
- 3Combine: 90 | 24 = 9024
- 496 × 94 = 9024 ✓
Numbers ABOVE 100 (excess instead of deficiency)
If a number is above 100, it has an excess instead of a deficiency. The same method applies — but with + instead of −.
- 103 × 104: excesses are 3 and 4
- Cross: 103 + 4 = 107 (ADD the other's excess)
- Units: 3 × 4 = 12 (2 digits, no padding needed)
- Combine: 107 | 12 = 10712
- 103 × 104 = 10712 ✓
Mix of above and below 100
If one number is below 100 and one is above, one has a deficiency (−) and one has an excess (+). The cross subtracts the deficiency and adds the excess. This is more complex — practise pure deficiency and pure excess cases first.
Forgetting to pad the units part
The most common error: 98 × 99 → deficiencies 2 and 1 → product = 2 → writing 982 instead of 9702. The units must be 02, not 2. Always ask: 'Is my units result 2 digits?'
- →Wrong: 98×99 → cross=97, units=2 → writes 972
- →Right: 98×99 → cross=97, units=02 → writes 9702. Check: 9702+... verifiable.
Challenge Round
Challenge: 97 × 95
Deficiencies are 3 and 5. Apply the full method. Don't forget to check your units padding.
Base-100 Nikhilam: same as base-10, but units must be 2 digits (pad with 0 if needed). For numbers above 100, use excess (add) instead of deficiency (subtract).
↪ Next: The Digit Sum Check — verify any answer instantly.
Key Points
முக்கிய குறிப்புகள்
- ✓Same method as base-10, but deficiency/excess is from 100
- ✓Units part must always be 2 digits — pad with 0 if needed
- ✓Numbers above 100: use excess (add) instead of deficiency (subtract)
- ✓Works for: 96×97, 103×104, 99×98, etc.
Glossary
சொல் அகராதி
Excess
மிகுதி
Base 100
100 அடிப்படை
Padding
நிரப்பு பூஜ்ஜியம்
Two-digit product
இரு இலக்க பெருக்கல்
Practice Activities
Quizவினாடி வினா
Answer each question to check your understanding.
For 98 × 96, what is the units part of the answer?