Class 5 Exam > Class 5 Notes > Math Olympiad for Class 5 > Olympiad Notes: Number Sense (7and 8 Digit Numbers)
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| Table of contents |
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| Introduction |
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| Place Value System |
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| Face Value and Place Value |
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| Successor and Predecessor |
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| Comparing Large Numbers |
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| Writing Numbers in Words |
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| Conversions |
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Introduction
Numbers can be very large. A 7-digit number is the number that has 7 digits. The smallest 7-digit number is 10,00,000 (ten lakh) and the largest is 99,99,999. An 8-digit number is the number that has 8 digits. The smallest 8-digit number is 1,00,00,000 (one crore) and the largest is 9,99,99,999.
Place Value System
The value of a digit depends on its position.
In the Indian Place Value System, we use commas like this: 1,23,45,678. The first comma comes after 3 digits from the right, and then commas are placed after every 2 digits. The order of places is: Ones, Tens, Hundreds, Thousands, Ten Thousands, Lakhs, Ten Lakhs, Crores.
Example: In 7,23,45,678
- 7 = Crore → 7,00,00,000
- 2 = Ten Lakh → 20,00,000
- 3 = Lakh → 3,00,000
- 4 = Ten Thousand → 40,000
- 5 = Thousand → 5,000
- 6 = Hundred → 600
- 7 = Ten → 70
- 8 = One → 8
Expanded form: 7,00,00,000 + 20,00,000 + 3,00,000 + 40,000 + 5,000 + 600 + 70 + 8
In the International Place Value System, commas are placed after every 3 digits from the right. For example: 72,345,678. The order of places is: Ones, Tens, Hundreds, Thousands, Ten Thousands, Hundred Thousands, Millions, Ten Millions.
Example: In 72,345,678
- 7 = Ten Million → 70,000,000
- 2 = Million → 2,000,000
- 3 = Hundred Thousand → 300,000
- 4 = Ten Thousand → 40,000
- 5 = Thousand → 5,000
- 6 = Hundred → 600
- 7 = Ten → 70
- 8 = One → 8
Expanded form: 70,000,000 + 2,000,000 + 300,000 + 40,000 + 5,000 + 600 + 70 + 8
Face Value and Place Value
The face value of a digit is the digit itself. The place value of a digit is the digit × its place.
Example: In 6,58,32,719
- Face value of 8 = 8
- Place value of 8 = 8,00,000 (since it is in the lakh place)
Successor and Predecessor
- The successor of a number is the number that comes just after it (add 1).
- The predecessor of a number is the number that comes just before it (subtract 1).
Examples:
- Successor of 54,32,100 = 54,32,101
- Predecessor of 70,00,000 = 69,99,999
Comparing Large Numbers
To compare numbers, start from the leftmost digit (highest place).
Example: Compare 6,45,23,178 and 6,54,23,178
- Both have 6 in the crore place → equal
- Compare next digit: 4 (ten lakh) and 5 (ten lakh) → 5 is bigger
So, 6,54,23,178 is greater.
Writing Numbers in Words
Numbers are read differently in Indian and International systems.
Examples:
- Indian: 4,56,78,901 → Four crore fifty-six lakh seventy-eight thousand nine hundred one
- International: 45,678,901 → Forty-five million six hundred seventy-eight thousand nine hundred one
Conversions
- 1 Lakh = 1,00,000
- 10 Lakhs = 10,00,000 = 1 Million
- 1 Crore = 1,00,00,000 = 10 Million
- 10 Crores = 10,00,00,000 = 100 Million = 1 Billion
The document Olympiad Notes: Number Sense (7and 8 Digit Numbers) | Math Olympiad for Class 5 is a part of the Class 5 Course Math Olympiad for Class 5.
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FAQs on Olympiad Notes: Number Sense (7and 8 Digit Numbers) - Math Olympiad for Class 5
| 1. What is the difference between face value and place value in a number? |  |
Ans. The face value of a digit is the value of the digit itself, regardless of its position in the number. For example, in the number 5,432, the face value of 4 is 4. The place value, on the other hand, depends on the position of the digit within the number. In the same example, the place value of 4 is 400, because it is in the hundreds place.
| 2. How can I find the successor and predecessor of a given number? | |
Ans. The successor of a number is the number that comes next in the counting order, which is found by adding 1. For example, the successor of 5,678 is 5,679. The predecessor is the number that comes before it, which is found by subtracting 1. Thus, the predecessor of 5,678 is 5,677.
| 3. What methods can be used to compare large numbers? | |
Ans. To compare large numbers, you can use the following methods: First, compare the number of digits; the number with more digits is larger. If both numbers have the same number of digits, compare the digits from left to right until you find a difference. The number with the larger digit in that position is the greater number. For example, 5,432 is greater than 5,321 because when comparing, 4 (in 5,432) is greater than 3 (in 5,321).
| 4. How do I write large numbers in words correctly? | |
Ans. To write large numbers in words, break the number down into groups of three digits starting from the right. For example, the number 1,234,567 is written as "one million two hundred thirty-four thousand five hundred sixty-seven." Always begin with the highest place value and work downwards, ensuring to include terms for each group.
| 5. What are the steps to convert numbers between different forms, such as standard form and expanded form? | |
Ans. To convert a number to expanded form, you break it down into the sum of each digit multiplied by its place value. For example, the number 4,256 in expanded form is 4,000 + 200 + 50 + 6. To convert from expanded form back to standard form, simply add the values together.
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Oct 07, 2025
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