Predecessor and Successor (Grade 5)
The predecessor of a number is the number that comes just before it on the number line. The successor is the number that comes just after it. In Class 5, students apply this concept to large numbers up to crores.
Finding predecessors and successors of large numbers requires careful handling of borrowing (when subtracting 1) and carrying (when adding 1), especially when numbers involve multiple zeroes or nines.
What is Predecessor and Successor - Class 5 Maths (Large Numbers)?
Predecessor: The number obtained by subtracting 1 from a given number. If the number is n, its predecessor is n − 1.
Successor: The number obtained by adding 1 to a given number. If the number is n, its successor is n + 1.
Key facts:
- Every whole number (except 0) has a predecessor.
- Every whole number has a successor.
- The predecessor of the successor of a number is the number itself.
- The successor of the predecessor of a number is the number itself.
Predecessor and Successor (Grade 5) Formula
Predecessor = Number − 1 | Successor = Number + 1
Solved Examples
Example 1: Example 1: Predecessor and successor of a 5-digit number
Problem: Find the predecessor and successor of 45,000.
Solution:
Predecessor: 45,000 − 1 = 44,999
Successor: 45,000 + 1 = 45,001
Example 2: Example 2: Predecessor of a lakh number
Problem: Find the predecessor of 1,00,000.
Solution:
1,00,000 − 1 = 99,999
Notice that the predecessor of the smallest 6-digit number is the largest 5-digit number.
Example 3: Example 3: Successor of a number with trailing nines
Problem: Find the successor of 9,99,999.
Solution:
9,99,999 + 1 = 10,00,000
The successor of the largest 6-digit number is the smallest 7-digit number (ten lakhs).
Example 4: Example 4: Large number in crores
Problem: Find the predecessor and successor of 5,00,00,000.
Solution:
Predecessor: 5,00,00,000 − 1 = 4,99,99,999
Successor: 5,00,00,000 + 1 = 5,00,00,001
Example 5: Example 5: Number ending in multiple zeroes
Problem: Find the predecessor of 30,00,000.
Solution:
30,00,000 − 1 = 29,99,999
When subtracting 1 from a number ending in zeroes, all the zeroes turn to 9 and the digit before them decreases by 1.
Example 6: Example 6: Successor of a 9-digit number
Problem: Find the successor of 10,00,00,000.
Solution:
10,00,00,000 + 1 = 10,00,00,001
Example 7: Example 7: Word problem — Ticket numbers
Problem: Priya's train ticket number is 4,56,230. What are the ticket numbers just before and just after hers?
Solution:
Predecessor: 4,56,230 − 1 = 4,56,229
Successor: 4,56,230 + 1 = 4,56,231
Answer: The ticket before is 4,56,229 and the ticket after is 4,56,231.
Example 8: Example 8: Finding a number between two given numbers
Problem: Find the number whose predecessor is 7,49,999 and verify by finding its successor.
Solution:
Step 1: If the predecessor is 7,49,999, then the number = 7,49,999 + 1 = 7,50,000
Step 2: Verify: Successor of 7,50,000 = 7,50,001. Predecessor of 7,50,000 = 7,49,999. Correct.
Answer: The number is 7,50,000
Example 9: Example 9: Predecessor of the smallest 8-digit number
Problem: What is the predecessor of the smallest 8-digit number?
Solution:
Step 1: The smallest 8-digit number = 1,00,00,000 (one crore).
Step 2: Predecessor = 1,00,00,000 − 1 = 99,99,999
This is the largest 7-digit number.
Answer: 99,99,999
Example 10: Example 10: Successor of the largest 8-digit number
Problem: What is the successor of the largest 8-digit number?
Solution:
Step 1: The largest 8-digit number = 9,99,99,999.
Step 2: Successor = 9,99,99,999 + 1 = 10,00,00,000 (ten crores).
This is the smallest 9-digit number.
Answer: 10,00,00,000
Key Points to Remember
- Predecessor = Number − 1; Successor = Number + 1.
- The predecessor of the smallest n-digit number is the largest (n−1)-digit number.
- The successor of the largest n-digit number is the smallest (n+1)-digit number.
- When subtracting 1 from a number ending in zeroes, all zeroes become 9 and the preceding digit decreases by 1.
- When adding 1 to a number ending in all 9s, all 9s become 0 and a new digit 1 is added at the front.
- A number lies between its predecessor and its successor on the number line.
- 0 has no predecessor in the whole number system.
Practice Problems
- Find the predecessor and successor of 8,00,000.
- Find the predecessor of 10,00,00,000.
- Find the successor of 49,99,999.
- What number has 23,45,677 as its predecessor?
- Find the predecessor of the smallest 7-digit number.
- Rahul's roll number is 1,00,000. What roll numbers come just before and after his?
- Find three consecutive numbers starting from the successor of 6,99,998.
- Find the predecessor and successor of 99,99,99,999.
Frequently Asked Questions
Q1. What is the predecessor of a number?
The predecessor of a number is the number that comes just before it. It is found by subtracting 1. For example, the predecessor of 500 is 499.
Q2. What is the successor of a number?
The successor of a number is the number that comes just after it. It is found by adding 1. For example, the successor of 500 is 501.
Q3. Does 0 have a predecessor?
In the whole number system, 0 does not have a predecessor because there is no whole number less than 0. In the integer system (studied in higher classes), the predecessor of 0 is −1.
Q4. What is the predecessor of 1,00,00,000?
The predecessor of 1,00,00,000 (one crore) is 99,99,999 (ninety-nine lakh ninety-nine thousand nine hundred ninety-nine). The smallest 8-digit number's predecessor is the largest 7-digit number.
Q5. Can two different numbers have the same successor?
No. Every number has a unique successor, and every number (except 0 in whole numbers) has a unique predecessor. If two numbers had the same successor, they would have to be the same number.
Q6. How do I find the predecessor of a number ending in many zeroes?
When you subtract 1 from a number like 40,00,000, all the trailing zeroes become 9s and the digit before them decreases by 1. So 40,00,000 − 1 = 39,99,999.
Q7. What happens when the successor has more digits than the original number?
This happens when the number is the largest n-digit number (all 9s). For example, successor of 99,999 is 1,00,000 — a 5-digit number becomes a 6-digit number. The 9s all become 0 and 1 is placed at the front.
Q8. Is this topic important for exams?
Yes. Finding predecessors and successors of large numbers is a frequently asked question in Class 5 CBSE exams and helps build understanding of the number line and place value system.
Related Topics
- Numbers up to Lakhs
- Comparing Large Numbers (Grade 5)
- Place Value of Large Numbers
- Indian and International Number System (Grade 5)
- Reading and Writing Large Numbers
- Ordering Large Numbers (Grade 5)
- Rounding Large Numbers
- Estimation (Grade 5)
- Roman Numerals (I to M)
- Numbers up to Crores
- Number Names in Lakhs and Crores
- Expanded Form of Large Numbers
