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Large Numbers Around Us - Of Crores and Crores!

Grade 7CBSE

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

🔑Concepts

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The Indian System of Numeration uses periods like Ones, Thousands, Lakhs, and Crores. Commas are placed after the first 33 digits from the right and then every 22 digits, e.g., 12,34,56,78912,34,56,789.

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The International System of Numeration uses periods like Ones, Thousands, and Millions. Commas are placed every 33 digits from the right, e.g., 123,456,789123,456,789.

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Conversion between systems: 1 crore=10 million1 \text{ crore} = 10 \text{ million}, 10 lakhs=1 million10 \text{ lakhs} = 1 \text{ million}, and 100 million=10 crores100 \text{ million} = 10 \text{ crores}.

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The Place Value of a digit depends on its position in the number, calculated as Face Value×Value of the place\text{Face Value} \times \text{Value of the place}, whereas the Face Value is the digit itself.

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Estimation or Rounding Off: To round to the nearest Lakh, look at the Ten-Thousands place. If it is 55 or more, increase the Lakhs digit by 11; otherwise, keep it the same and replace following digits with 00.

📐Formulae

1 Crore=1,00,00,000=1071 \text{ Crore} = 1,00,00,000 = 10^7

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

1 Billion=1,000,000,000=1091 \text{ Billion} = 1,000,000,000 = 10^9

Place Value=Face Value×Position Value\text{Place Value} = \text{Face Value} \times \text{Position Value}

💡Examples

Problem 1:

Write the number 7452309874523098 in the Indian System with commas and find the place value of the digit 44.

Solution:

In the Indian System: 7,45,23,0987,45,23,098. Place value of 44: 4×10,00,000=40,00,0004 \times 10,00,000 = 40,00,000.

Explanation:

We place commas after the hundreds, ten-thousands, and ten-lakhs places. The digit 44 is in the ten-lakhs place, so its place value is 40 lakhs40 \text{ lakhs}.

Problem 2:

Solve the following addition: 4,50,00,000+2,35,00,0004,50,00,000 + 2,35,00,000.

Solution:

45000000+2350000068500000\begin{array}{r} 45000000 \\ + 23500000 \\ \hline 68500000 \end{array}

Explanation:

Align the digits according to their place values (Crores, Ten-lakhs, etc.) and add column by column from right to left.

Problem 3:

Find the difference between 8 crores8 \text{ crores} and 3,45,67,8923,45,67,892.

Solution:

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

Explanation:

We subtract 3,45,67,8923,45,67,892 from 8,00,00,0008,00,00,000 by borrowing from the higher place values where necessary.

Problem 4:

Estimate the sum of 5,2905,290 and 17,98617,986 by rounding off to the nearest thousands.

Solution:

18,000+5,000=23,00018,000 + 5,000 = 23,000

Explanation:

17,98617,986 rounded to the nearest thousand is 18,00018,000 (since the hundreds digit 9>59 > 5). 5,2905,290 rounded to the nearest thousand is 5,0005,000 (since 2<52 < 5).