krit.club logo

Knowing Our Numbers - Place Value and Use of Commas

Grade 6CBSE

Review the key concepts, formulae, and examples before starting your quiz.

🔑Concepts

•

Place Value and Face Value: Every digit in a number has two values. The face value is the digit itself (e.g., the face value of 55 in 5,4325,432 is 55), while the place value depends on its position in the number. Visualize a place value chart where moving one place to the left increases the value by 1010 times. For example, in 5,4325,432, the 55 is in the thousands place, so its place value is 5imes1,000=5,0005 imes 1,000 = 5,000.

•

Indian System of Numeration: This system uses periods of Ones, Thousands, Lakhs, and Crores. Visually, commas are used to mark these periods. Starting from the right, the first comma comes after three digits (hundreds place), and subsequent commas come after every two digits. The pattern of digits between commas looks like 2,2,32,2,3 (e.g., 12,34,56,78912,34,56,789).

•

International System of Numeration: This system uses periods of Ones, Thousands, and Millions. Visually, commas are placed after every three digits starting from the right. The pattern is a consistent 3,3,33,3,3 (e.g., 123,456,789123,456,789). One million is written as 1,000,0001,000,000.

•

Expansion of Numbers: To expand a number, we write the sum of the products of each digit and its place value. Imagine stretching the number out to see the value of each part. For example, 78,29378,293 is expanded as 7imes10,000+8imes1,000+2imes100+9imes10+3imes17 imes 10,000 + 8 imes 1,000 + 2 imes 100 + 9 imes 10 + 3 imes 1.

•

Comparison of Numbers: To compare two numbers, first count the number of digits. The number with more digits is greater. If the number of digits is the same, compare the leftmost digits. If they are the same, move to the next digit to the right until a difference is found. Visually, you can line up numbers vertically by their place values to compare them easily.

•

Relationship between Systems: It is important to know how the Indian and International systems relate. For instance, 1 million=10 lakhs1 \text{ million} = 10 \text{ lakhs} and 10 millions=1 crore10 \text{ millions} = 1 \text{ crore}. Visualizing a combined chart helps see that the 'Ten Lakhs' column in the Indian system aligns with the 'Millions' column in the International system.

📐Formulae

Place Value=Face Value×Value of the position\text{Place Value} = \text{Face Value} \times \text{Value of the position}

1 Lakh=100,000=1051 \text{ Lakh} = 100,000 = 10^5

1 Million=1,000,000=1061 \text{ Million} = 1,000,000 = 10^6

1 Crore=10,000,000=107=100 Lakhs1 \text{ Crore} = 10,000,000 = 10^7 = 100 \text{ Lakhs}

1 Billion=1,000,000,000=109=1,000 Millions1 \text{ Billion} = 1,000,000,000 = 10^9 = 1,000 \text{ Millions}

💡Examples

Problem 1:

Insert commas and write the number name for 8759576287595762 according to the Indian System of Numeration.

Solution:

Step 1: Identify the periods from the right. The first period (Ones) has 33 digits (762762), the second (Thousands) has 22 digits (9595), the third (Lakhs) has 22 digits (7575), and the fourth (Crores) has the remaining digits (88). Step 2: Place commas: 8,75,95,7628,75,95,762. Step 3: Write the name: Eight crore, seventy-five lakh, ninety-five thousand, seven hundred sixty-two.

Explanation:

In the Indian system, we group digits in a 3,2,23,2,2 pattern from the right to represent Hundreds, Thousands, Lakhs, and Crores.

Problem 2:

Write the expanded form and the International number name for 7000250970002509.

Solution:

Step 1: Place commas every three digits from the right: 70,002,50970,002,509. Step 2: Expanded form: 7×10,000,000+0×1,000,000+0×100,000+0×10,000+2×1,000+5×100+0×10+9×17 \times 10,000,000 + 0 \times 1,000,000 + 0 \times 100,000 + 0 \times 10,000 + 2 \times 1,000 + 5 \times 100 + 0 \times 10 + 9 \times 1. Simplified Expansion: 7,00,00,000+2,000+500+97,00,00,000 + 2,000 + 500 + 9. Step 3: International Name: Seventy million, two thousand, five hundred nine.

Explanation:

The International system groups digits into 'Millions' and 'Thousands' using commas every three places. Zeros are skipped in the verbal number name but represent place holders in expansion.