Olympiad Notes: Number Sense (7and 8 Digit Numbers) | Math Olympiad for Class 5 PDF Download

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