Place values in whole numbers

key notes:

Definition of Place Value:

Place value refers to the value of a digit based on its position in a number, with each position representing a specific value.

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Place Values in the Indian System:

• The first group consists of three digits (units, tens, hundreds).
• Subsequent groups consist of two digits each (thousands, lakhs, crores).

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Place Value Chart:

• Units: Ones (1), Tens (10), Hundreds (100)
• Thousands: Thousands (1,000), Ten Thousands (10,000)
• Lakhs: Lakhs (1,00,000), Ten Lakhs (10,00,000)
• Crores: Crores (1,00,00,000), Ten Crores (10,00,00,000)

Crores	Ten lakhs	Lakhs	Ten Thousands	Thousands	Hundreds	Tens	Ones
9	8	7	6	5	4	3	2

Reading the Number:

• 9 Crores
• 87 Lakhs
• 65 Thousands
• 432 (Hundreds, Tens, and Ones combined)

Example: 9,87,65,432 is read as “Nine crores eighty-seven lakhs sixty-five thousand four hundred thirty-two.”

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Reading Numbers:

Read the number by separating it into groups:

Example: 23,45,678 is read as Twenty-three lakh forty-five thousand six hundred seventy-eight.

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Writing Numbers:

When writing large numbers, use commas to separate the groups according to the Indian system:

Example: 1,23,45,678 (One crore twenty-three lakh forty-five thousand six hundred seventy-eight).

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Understanding Values:

Each place represents a value that is ten times the value of the place to its right:

Example: In the number 5,23,45,678:

• 5 is in the crores place.
• 2 is in the ten lakhs place.
• 3 is in the lakhs place.
• 4 is in the ten thousands place.
• 5 is in the thousands place.
• 6 is in the hundreds place.
• 7 is in the tens place.
• 8 is in the ones place.

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Practice with Examples:

Give students practice problems to identify and write numbers according to the Indian place value system:

Example:

• Identify the place value of each digit in 7,89,23,456.
• Identify the place value of each digit in 9,23,456.
• Identify the place value of each digit in 25,23,125.

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Comparison with International System:

Highlight the differences between the Indian and International place value systems to ensure clarity.

Key Differences

Grouping of Digits:

• Indian System: Groups digits as three, two, two (e.g., 7,89,23,456).
• International System: Groups digits in sets of three (e.g., 78,923,456).

Terminology:

• Indian System: Uses lakhs and crores.
• International System: Uses millions and billions.

Usage:

• Indian System: Predominantly used in India.
• International System: Used globally in most other countries.

Practice Examples

1. Convert between Systems:
   • Indian: 12,34,56,789
   • International: 123,456,789
2. Identify Place Values:
   • Number: 6,78,90,123
   • Indian: 6 crores 78 lakhs 90 thousand 123
   • International: 67 million 890 thousand 123
3. Write Numbers:
   • Write forty-three million, twenty-one thousand, nine hundred eighty-seven.
   • Indian: 4,32,10,987
   • International: 43,210,987

Learn with an example

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Let’s practice!