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Large Numbers - Place Value up to 8 digits

Grade 5CBSE

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

🔑Concepts

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The Indian Place Value System: To read and write numbers up to 8 digits, we use the Indian system. The places are grouped into periods. For an 8-digit number, the periods are Crores, Lakhs, Thousands, and Ones. Visualise a table from right to left: Ones Period (Ones, Tens, Hundreds), Thousands Period (Thousands, Ten-Thousands), Lakhs Period (Lakhs, Ten-Lakhs), and Crores Period (Crores).

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Understanding 8-digit Numbers: An 8-digit number begins at the Crores place. The smallest 8-digit number is 1,00,00,0001,00,00,000 (One Crore) and the largest 8-digit number is 9,99,99,9999,99,99,999 (Nine Crore Ninety-Nine Lakh Ninety-Nine Thousand Nine Hundred Ninety-Nine).

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Use of Commas (Periods): Commas are used to separate periods to make reading easier. In the Indian system, the first comma is placed after the hundreds place (3 digits from the right), and subsequent commas are placed after every 2 digits. For example, 88 digits are grouped as C,TL,L,TTh,Th,H,T,OC,TL,L,TTh,Th,H,T,O or 1,23,45,6781,23,45,678.

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Place Value vs. Face Value: The 'Face Value' of a digit is the digit itself (it never changes). The 'Place Value' of a digit depends on its position in the number. For example, in the number 5,67,00,0005,67,00,000, the face value of 55 is 55, but its place value is 5×1,00,00,000=5,00,00,0005 \times 1,00,00,000 = 5,00,00,000.

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Expanded Form: Writing a number as the sum of the place values of all its digits. Visualise this as stretching the number out. For example, 2,45,60,1232,45,60,123 is written as 2,00,00,000+40,00,000+5,00,000+60,000+0+100+20+32,00,00,000 + 40,00,000 + 5,00,000 + 60,000 + 0 + 100 + 20 + 3.

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Successor and Predecessor: The successor is the number that comes immediately after a given number (Number +1+ 1). The predecessor is the number that comes immediately before a given number (Number −1- 1).

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Comparing Large Numbers: To compare two 8-digit numbers, start from the leftmost place (Crores). If the digits are the same, move to the next place on the right (Ten-Lakhs) and continue until you find different digits. The number with the greater digit at that place is the larger number.

📐Formulae

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

Successor=Number+1\text{Successor} = \text{Number} + 1

Predecessor=Number−1\text{Predecessor} = \text{Number} - 1

1 Crore=100 Lakhs=10,000,0001 \text{ Crore} = 100 \text{ Lakhs} = 10,000,000

💡Examples

Problem 1:

Write the number 5,40,26,7195,40,26,719 in expanded form and state the place value of the digit 44.

Solution:

Step 1: Identify the place of each digit.

  • 55 is at the Crores place: 5,00,00,0005,00,00,000
  • 44 is at the Ten-Lakhs place: 40,00,00040,00,000
  • 00 is at the Lakhs place: 00
  • 22 is at the Ten-Thousands place: 20,00020,000
  • 66 is at the Thousands place: 6,0006,000
  • 77 is at the Hundreds place: 700700
  • 11 is at the Tens place: 1010
  • 99 is at the Ones place: 99

Step 2: Write as a sum for expanded form. Expanded Form: 5,00,00,000+40,00,000+0+20,000+6,000+700+10+95,00,00,000 + 40,00,000 + 0 + 20,000 + 6,000 + 700 + 10 + 9

Step 3: Determine the place value of 44. Place value of 4=4×10,00,000=40,00,0004 = 4 \times 10,00,000 = 40,00,000.

Explanation:

We use the Indian place value chart to assign values to each digit based on its position and then sum them up for the expanded form.

Problem 2:

Find the difference between the place value and face value of the digit 77 in the number 8,72,15,4308,72,15,430.

Solution:

Step 1: Find the face value of 77. The face value is the digit itself, so face value =7= 7.

Step 2: Find the place value of 77. In 8,72,15,4308,72,15,430, the digit 77 is in the Ten-Lakhs place. Place value =7×10,00,000=70,00,000= 7 \times 10,00,000 = 70,00,000.

Step 3: Calculate the difference. Difference =70,00,000−7=69,99,993= 70,00,000 - 7 = 69,99,993.

Explanation:

The place value is determined by the digit's position (Ten-Lakhs), while the face value remains the digit itself. Subtracting the two gives the required difference.