Predecessor and Successor of Large Numbers
You already know that the successor of a number is the number that comes just after it (number + 1), and the predecessor is the number that comes just before it (number − 1). This concept works the same way for large numbers — lakhs, ten-lakhs, crores, and beyond.
Finding predecessors and successors of large numbers helps you understand the number system better, especially when numbers change at place-value boundaries (like 99,999 → 1,00,000 or 9,99,999 → 10,00,000).
This is a quick and useful skill for Class 6 students working with the Indian and International number systems.
What is Predecessor and Successor of Large Numbers?
Definitions:
- Successor of a number = the number + 1 (the next number).
- Predecessor of a number = the number − 1 (the previous number).
For large numbers, the same rule applies:
- Successor of 4,56,789 = 4,56,789 + 1 = 4,56,790
- Predecessor of 4,56,789 = 4,56,789 − 1 = 4,56,788
Key tip: The most interesting cases are when numbers are at boundaries:
- Successor of 99,999 = 1,00,000 (five digits to six digits!)
- Predecessor of 1,00,000 = 99,999 (six digits to five digits!)
- Successor of 9,99,999 = 10,00,000 (six digits to seven digits!)
Types and Properties
1. Simple Cases
When adding or subtracting 1 does not change the number of digits.
- Successor of 3,45,678 = 3,45,679.
- Predecessor of 7,89,012 = 7,89,011.
2. Boundary Cases (Carrying Over)
When the last digits are all 9s, adding 1 causes a carry:
- Successor of 2,99,999 = 3,00,000.
- Successor of 9,99,999 = 10,00,000.
3. Boundary Cases (Borrowing)
When subtracting 1 from a number ending in 0s:
- Predecessor of 5,00,000 = 4,99,999.
- Predecessor of 10,00,000 = 9,99,999.
4. Very Large Numbers
- Successor of 1,00,00,000 (1 crore) = 1,00,00,001.
- Predecessor of 1,00,00,000 = 99,99,999.
Solved Examples
Example 1: Example 1: Simple successor
Problem: Find the successor of 5,67,834.
Solution:
- 5,67,834 + 1 = 5,67,835.
Answer: 5,67,835
Example 2: Example 2: Simple predecessor
Problem: Find the predecessor of 8,45,210.
Solution:
- 8,45,210 − 1 = 8,45,209.
Answer: 8,45,209
Example 3: Example 3: Boundary successor
Problem: Find the successor of 99,999.
Solution:
- 99,999 + 1 = 1,00,000.
- The number jumps from 5 digits to 6 digits.
Answer: 1,00,000 (one lakh)
Example 4: Example 4: Boundary predecessor
Problem: Find the predecessor of 10,00,000.
Solution:
- 10,00,000 − 1 = 9,99,999.
- The number drops from 7 digits to 6 digits.
Answer: 9,99,999
Example 5: Example 5: Large number successor
Problem: Find the successor of 9,99,999.
Solution:
- 9,99,999 + 1 = 10,00,000 (ten lakh).
Answer: 10,00,000
Example 6: Example 6: Large number predecessor
Problem: Find the predecessor of 1,00,00,000.
Solution:
- 1,00,00,000 − 1 = 99,99,999.
Answer: 99,99,999
Example 7: Example 7: Both predecessor and successor
Problem: Find both predecessor and successor of 5,00,000.
Solution:
- Predecessor = 5,00,000 − 1 = 4,99,999.
- Successor = 5,00,000 + 1 = 5,00,001.
Answer: Predecessor = 4,99,999. Successor = 5,00,001.
Example 8: Example 8: International system
Problem: Find the successor of 999,999 (international system).
Solution:
- 999,999 + 1 = 1,000,000 (one million).
Answer: 1,000,000
Example 9: Example 9: Between two numbers
Problem: A number's predecessor is 7,49,999 and its successor is 7,50,001. What is the number?
Solution:
- The number is between 7,49,999 and 7,50,001.
- Number = 7,49,999 + 1 = 7,50,000.
Answer: 7,50,000
Example 10: Example 10: Successor chain
Problem: Write 3 successors of 9,99,997.
Solution:
- 9,99,997 → 9,99,998 → 9,99,999 → 10,00,000.
Answer: 9,99,998; 9,99,999; 10,00,000.
Real-World Applications
Counting: Understanding successor and predecessor is the basis of counting forward and backward with large numbers.
Number Patterns: Recognising what comes before and after helps identify patterns in number sequences.
Odometer Readings: A car odometer showing 99,999 km will show 1,00,000 km after 1 more km — a successor at a boundary.
Population: Census data often involves large numbers. Knowing predecessors and successors helps read and compare population figures.
Banking: Account numbers, transaction IDs, and serial numbers all use large numbers where predecessor and successor understanding is helpful.
Key Points to Remember
- Successor = number + 1. Predecessor = number − 1.
- This rule works for all numbers, no matter how large.
- Boundary cases: successor of 99,999 = 1,00,000 (digit count changes).
- Predecessor of 1,00,000 = 99,999 (digit count changes).
- Every whole number (except 0) has a predecessor. Every whole number has a successor.
- 0 has no predecessor in whole numbers (but −1 in integers).
- The difference between a number's successor and predecessor is always 2.
- A number is always the average of its predecessor and successor.
Practice Problems
- Find the successor of: (a) 4,89,999, (b) 99,99,999, (c) 7,00,000.
- Find the predecessor of: (a) 3,00,000, (b) 10,00,000, (c) 56,78,901.
- A number's predecessor is 9,99,999. What is the number? What is its successor?
- Write 4 successors of 9,99,996.
- Find both predecessor and successor of: (a) 1,00,000, (b) 50,00,000.
- The odometer of a car shows 99,999 km. What will it show after 1 km? After 2 km?
- What is the predecessor of the smallest 7-digit number?
- Find the successor of the largest 6-digit number.
Frequently Asked Questions
Q1. What is the successor of a number?
The successor is the number that comes right after it. Add 1 to find the successor. Successor of 50 is 51. Successor of 9,99,999 is 10,00,000.
Q2. What is the predecessor of a number?
The predecessor is the number that comes right before it. Subtract 1. Predecessor of 50 is 49. Predecessor of 1,00,000 is 99,999.
Q3. Does 0 have a predecessor?
In whole numbers, no — 0 is the smallest whole number. In integers, the predecessor of 0 is −1.
Q4. What happens at boundary numbers like 99,999?
When all digits are 9, adding 1 causes a carry through all places, increasing the digit count. 99,999 + 1 = 1,00,000 (5 digits become 6 digits).
Q5. What is the successor of the largest 6-digit number?
The largest 6-digit number is 9,99,999. Its successor is 10,00,000 (the smallest 7-digit number).
Q6. What is the predecessor of the smallest 7-digit number?
The smallest 7-digit number is 10,00,000. Its predecessor is 9,99,999 (the largest 6-digit number).
Q7. What is the difference between successor and predecessor?
Successor = number + 1. Predecessor = number − 1. The difference between the successor and predecessor of any number is always 2.
Q8. Can a number be its own successor?
No. The successor is always 1 more than the number, so it can never equal the number itself.
