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Large Numbers Around Us - Land of Tens

Grade 7CBSE

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

🔑Concepts

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In the 'Land of Tens' (the Decimal System), the value of a digit increases by 1010 times as it moves one place to the left. For example, 1 Thousand=10×1 Hundred1 \text{ Thousand} = 10 \times 1 \text{ Hundred}.

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The Indian System of Numeration uses place values: Units, Tens, Hundreds, Thousands, Ten Thousands, Lakhs, Ten Lakhs, Crores, and Ten Crores. Commas are placed as: 9,87,65,4329,87,65,432.

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The International System of Numeration uses place values: Units, Tens, Hundreds, Thousands, Ten Thousands, Hundred Thousands, Millions, Ten Millions, Hundred Millions, and Billions. Commas are placed as: 98,765,43298,765,432.

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To convert between systems: 1 Million=10 Lakhs1 \text{ Million} = 10 \text{ Lakhs}, 10 Millions=1 Crore10 \text{ Millions} = 1 \text{ Crore}, and 1 Billion=100 Crores1 \text{ Billion} = 100 \text{ Crores}.

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Expanded form of a number represents the sum of the values of each digit. For example, 5,432=(5×103)+(4×102)+(3×101)+(2×100)5,432 = (5 \times 10^3) + (4 \times 10^2) + (3 \times 10^1) + (2 \times 10^0).

📐Formulae

101=1010^1 = 10

102=10010^2 = 100

103=1,000 (One Thousand)10^3 = 1,000 \text{ (One Thousand)}

105=1,00,000 (One Lakh)10^5 = 1,00,000 \text{ (One Lakh)}

106=1,000,000 (One Million)10^6 = 1,000,000 \text{ (One Million)}

107=1,00,00,000 (One Crore)10^7 = 1,00,00,000 \text{ (One Crore)}

109=1,000,000,000 (One Billion)10^9 = 1,000,000,000 \text{ (One Billion)}

💡Examples

Problem 1:

Write the number 7,34,5127,34,512 in expanded form using powers of 1010.

Solution:

7×105+3×104+4×103+5×102+1×101+2×1007 \times 10^5 + 3 \times 10^4 + 4 \times 10^3 + 5 \times 10^2 + 1 \times 10^1 + 2 \times 10^0

Explanation:

Identify the place value of each digit: 77 is in Lakhs (10510^5), 33 is in Ten Thousands (10410^4), 44 is in Thousands (10310^3), 55 is in Hundreds (10210^2), 11 is in Tens (10110^1), and 22 is in Ones (10010^0).

Problem 2:

Convert 5050 Million into the Indian system of numeration.

Solution:

5 Crores5 \text{ Crores}

Explanation:

Since 10 Million=1 Crore10 \text{ Million} = 1 \text{ Crore}, then 50 Million=5×10 Million=5×1 Crore=5 Crores50 \text{ Million} = 5 \times 10 \text{ Million} = 5 \times 1 \text{ Crore} = 5 \text{ Crores}.

Problem 3:

Subtract 3,45,67,8923,45,67,892 from 8,00,00,0008,00,00,000.

Solution:

80000000−3456789245432108\begin{array}{r} 80000000 \\ -34567892 \\ \hline 45432108 \end{array}

Explanation:

Perform the subtraction by borrowing across the zeros. The result is 4,54,32,1084,54,32,108 (Four crore fifty-four lakh thirty-two thousand one hundred and eight).