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Number System - Large Numbers up to 6 digits

Grade 4ICSE

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

🔑Concepts

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A 6-digit number extends to the Lakhs place. Imagine a place value chart with columns from right to left: Ones (OO), Tens (TT), Hundreds (HH), Thousands (ThTh), Ten Thousands (TThTTh), and Lakhs (LL). For example, the number 1,00,0001,00,000 is read as One Lakh and is the smallest 6-digit number.

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Place Value vs. Face Value: The face value of a digit is the digit itself, whereas the Place Value depends on its position in the number. In the number 5,67,8905,67,890, the face value of 66 is 66, but its place value is 6×10,000=60,0006 \times 10,000 = 60,000 because it is in the Ten Thousands column.

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Indian System Periods: Commas are used to group digits into periods to make large numbers easier to read. The first comma is placed after the Hundreds place (3 digits from the right), and subsequent commas are placed every 2 digits. Example: 5,43,2105,43,210 shows the 'Lakhs', 'Thousands', and 'Ones' periods clearly.

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Expanded Form: This is writing the number as the sum of the place values of each of its digits. Visualizing 3,42,1053,42,105 as 3,00,000+40,000+2,000+100+0+53,00,000 + 40,000 + 2,000 + 100 + 0 + 5 helps understand the total value contributed by each digit's position.

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Comparing Large Numbers: To compare two numbers, first count the number of digits; the number with more digits is greater. If the number of digits is equal, compare the digits starting from the leftmost place (Lakhs). For instance, in 4,56,7894,56,789 and 4,57,1004,57,100, the Lakhs and Ten Thousands digits are identical, but since 7>67 > 6 in the Thousands place, 4,57,100>4,56,7894,57,100 > 4,56,789.

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Successor and Predecessor: The number that comes immediately after a given number is its Successor (+1+1), and the number that comes immediately before it is its Predecessor (−1-1). For 9,99,9999,99,999 (the largest 6-digit number), the predecessor is 9,99,9989,99,998 and the successor is 10,00,00010,00,000 (a 7-digit number).

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Forming Numbers from Digits: To form the greatest number, arrange the given digits in descending order. To form the smallest number, arrange them in ascending order. Note that 00 cannot be placed at the highest place value; for the digits 4,0,7,24, 0, 7, 2, the smallest 4-digit number is 2,0472,047, not 0,2470,247.

📐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

6-digit Standard Form:L,TTh,Th,H,T,O\text{6-digit Standard Form}: L, TTh, Th, H, T, O

Expanded Form of abc,def=(a×1,00,000)+(b×10,000)+(c×1,000)+(d×100)+(e×10)+(f×1)\text{Expanded Form of } abc,def = (a \times 1,00,000) + (b \times 10,000) + (c \times 1,000) + (d \times 100) + (e \times 10) + (f \times 1)

💡Examples

Problem 1:

Write the expanded form and the number name for 5,32,1095,32,109.

Solution:

  1. Identify the place values for each digit: 55 is at Lakhs, 33 at Ten Thousands, 22 at Thousands, 11 at Hundreds, 00 at Tens, and 99 at Ones. \ 2. Expanded form: 5,00,000+30,000+2,000+100+0+95,00,000 + 30,000 + 2,000 + 100 + 0 + 9. \ 3. Number name: Five lakh, thirty-two thousand, one hundred and nine.

Explanation:

To solve this, we break down the number according to the Indian Place Value system and then write out the sum of those values and their word equivalents.

Problem 2:

Find the difference between the place value of 88 and the face value of 88 in the number 8,43,2108,43,210.

Solution:

  1. Identify the position of 88: It is in the Lakhs place. \ 2. Calculate the place value: 8×1,00,000=8,00,0008 \times 1,00,000 = 8,00,000. \ 3. Identify the face value: The face value of 88 is simply 88. \ 4. Calculate the difference: 8,00,000−8=7,99,9928,00,000 - 8 = 7,99,992.

Explanation:

This problem tests the understanding of the distinction between a digit's position (place value) and its actual value (face value).