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What is System of Numeration?

A numeral system is a writing system for expressing numbers; that is, a mathematical notation for representing numbers of a given set, using digits or other symbols in a consistent manner. The same sequence of symbols may represent different numbers in different numeral systems.More Than a Million Chapter Notes - Class 5

Indian System of Numeration

In the Indian system, numbers are grouped into different periods: Ones, Thousands, Lakhs, and Crores. Each period is separated by commas. Here is the structure:

  • Ones: This includes the places for Ones, Tens, and Hundreds.
  • Thousands: This includes the places for Thousands and Ten Thousands.
  • Lakhs: This includes the places for Lakhs and Ten Lakhs.
  • Crores: This includes the places for Crores and Ten Crores.

Place Values in the Indian System:

  1. Ones (1)
  2. Tens (10)
  3. Hundreds (100)
  4. Thousands (1,000)
  5. Ten Thousands (10,000)
  6. Lakhs (1,00,000)
  7. Ten Lakhs (10,00,000)
  8. Crores (1,00,00,000)
  9. Ten Crores (10,00,00,000)More Than a Million Chapter Notes - Class 5

International System of Numeration

In the International system, numbers are grouped into periods of three digits each. These periods are Millions, Thousands, and Ones. Each period is separated by commas. Here is the structure:

  • Ones: This includes the places for Ones, Tens, and Hundreds.
  • Thousands: This includes the places for Thousands, Ten Thousands, and Hundred Thousands.
  • Millions: This includes the places for Millions, Ten Millions, and Hundred Millions.

Place Values in the International System:

  1. Ones (1)
  2. Tens (10)
  3. Hundreds (100)
  4. Thousands (1,000)
  5. Ten Thousands (10,000)
  6. Hundred Thousands (100,000)
  7. Millions (1,000,000)
  8. Ten Millions (10,000,000)
  9. Hundred Millions (100,000,000)

Writing Numbers in Both Systems

Example 1: The Number 5,673,899

In the Indian System:

  • Written as: 56,73,899
  • In words: Fifty-six lakh seventy-three thousand eight hundred ninety-nine

In the International System:

  • Written as: 5,673,899
  • In words: Five million six hundred seventy-three thousand eight hundred ninety-nine

Example 2: A Larger Number 5,678,932,156

In the Indian System:

  • Written as: 5,67,89,32,156
  • In words: Five crore sixty-seven lakh eighty-nine thousand thirty-two hundred fifty-six

In the International System:

  • Written as: 5,678,932,156
  • In words: Five billion six hundred seventy-eight million nine hundred thirty-two thousand one hundred fifty-six

Using Large Numbers

Large numbers are often used in contexts like population, financial data, and large-scale measurements.

Example: Population

The population of a country as of 31 March 2016 was 1,210,193,422.

In the International System:

  • Written as: 1,210,193,422
  • In words: One billion two hundred ten million one hundred ninety-three thousand four hundred twenty-two

In Expanded Notation:

  • 1 x 1,000,000,000 (One Billion)
  • 210 x 1,000,000 (Two Hundred Ten Million)
  • 193 x 1,000 (One Hundred Ninety-Three Thousand)
  • 4 x 100 (Four Hundred)
  • 2 x 10 (Twenty)
  • 2 x 1 (Two)

Relationship Between Indian and International Systems

To understand the relationship, we compare the equivalent values in both systems:

  • 100,000 (Indian: 1 Lakh) = 1,00,000
  • 1,000,000 (Indian: 10 Lakh) = 10,00,000
  • 10,000,000 (Indian: 1 Crore) = 1,00,00,000
  • 1 Billion = 1,000,000,000
  • 1 Trillion = 1,000,000,000,000

Expanded Notation of Numbers

Example: The Number 5,678,901

In Expanded Notation:

  • (5 x 1,000,000) + (678 x 1,000) + (9 x 100) + (0 x 10) + (1 x 1)
  • In words: Five million six hundred seventy-eight thousand nine hundred one

Example: The Number 18,764,325

In Expanded Notation:

  • (18 x 1,000,000) + (764 x 1,000) + (3 x 100) + (2 x 10) + (5 x 1)
  • In words: Eighteen million seven hundred sixty-four thousand three hundred twenty-five

Key Points to Remember

  • 100,000 = 1 Lakh
  • 1 Million = 10 Lakhs
  • 10 Million = 1 Crore
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FAQs on More Than a Million Chapter Notes - Class 5

1. What is the Indian System of Numeration?
Ans. The Indian System of Numeration is a place value system that uses lakh and crore as the higher denominations for grouping numbers in thousands and millions respectively.
2. What is the International System of Numeration?
Ans. The International System of Numeration, also known as the Western System, is a place value system that uses million, billion, and trillion as the higher denominations for grouping numbers.
3. What is the relationship between the Indian and International Systems of Numeration?
Ans. The Indian and International Systems of Numeration both follow a place value system but have different higher denominations for grouping numbers. The Indian system uses lakh and crore, while the International system uses million, billion, and trillion.
4. How do you convert numbers between the Indian and International Systems of Numeration?
Ans. To convert numbers between the Indian and International Systems of Numeration, you can use the following conversions: 1 crore = 10 million, 1 lakh = 100,000, 1 billion = 100 crore, and 1 trillion = 1 lakh crore.
5. Why is it important to understand both the Indian and International Systems of Numeration?
Ans. Understanding both the Indian and International Systems of Numeration is important for communication and business transactions as different countries and regions may use different systems. It helps in avoiding confusion and ensures accurate representation of large numbers.
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