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Large Numbers Around Us - A Lakh Varieties!

Grade 7CBSE

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

🔑Concepts

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Understanding the Indian Place Value System: It follows the pattern of Ones, Tens, Hundreds, Thousands, Ten Thousands, Lakhs, Ten Lakhs, Crores, and Ten Crores. Commas are placed after the hundreds place and then after every two digits, e.g., 7,34,50,0007,34,50,000.

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Understanding the International Place Value System: It follows the pattern of Ones, Tens, Hundreds, Thousands, Ten Thousands, Hundred Thousands, Millions, Ten Millions, and Hundred Millions. Commas are placed after every three digits from the right, e.g., 73,450,00073,450,000.

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Conversion between systems: 1 million=10 lakhs1 \text{ million} = 10 \text{ lakhs} and 1 crore=10 millions1 \text{ crore} = 10 \text{ millions}.

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Estimation: Rounding off numbers to the nearest tens, hundreds, or thousands to simplify calculations. For example, 4,8274,827 rounded to the nearest thousand is 5,0005,000.

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Large Number Operations: Performing addition, subtraction, multiplication, and division with numbers exceeding 1,00,0001,00,000.

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Measurement Conversions: Using large numbers to convert units, such as 1 km=1,00,000 cm1 \text{ km} = 1,00,000 \text{ cm} and 1 kg=10,00,000 mg1 \text{ kg} = 10,00,000 \text{ mg}.

📐Formulae

1 Lakh=100 Thousands=1,00,0001 \text{ Lakh} = 100 \text{ Thousands} = 1,00,000

1 Crore=100 Lakhs=1,00,00,0001 \text{ Crore} = 100 \text{ Lakhs} = 1,00,00,000

1 Million=10 Lakhs1 \text{ Million} = 10 \text{ Lakhs}

1 Billion=1,000 Millions=100 Crores1 \text{ Billion} = 1,000 \text{ Millions} = 100 \text{ Crores}

1 km=1000 m=1,00,000 cm=10,00,000 mm1 \text{ km} = 1000 \text{ m} = 1,00,000 \text{ cm} = 10,00,000 \text{ mm}

💡Examples

Problem 1:

A vessel has 44 litres and 500500 ml of curd. In how many glasses, each of 2525 ml capacity, can it be filled?

Solution:

Total curd = 44 litres 500500 ml = (4×1000)+500=4500(4 \times 1000) + 500 = 4500 ml. Capacity of one glass = 2525 ml. Number of glasses = 4500÷254500 \div 25.

Explanation:

4500÷25=1804500 \div 25 = 180. Therefore, 180180 glasses can be filled.

Problem 2:

Estimate the sum 5,290+17,9865,290 + 17,986 by rounding off to the nearest thousands.

Solution:

17,98617,986 rounds off to 18,00018,000. 5,2905,290 rounds off to 5,0005,000. Estimated sum = 18,000+5,000=23,00018,000 + 5,000 = 23,000.

Explanation:

Since the hundreds digit in 17,98617,986 is 99 (which is >5>5), we round up. In 5,2905,290, the hundreds digit is 22 (which is <5<5), so we round down.

Problem 3:

Find the difference between the greatest and the least 55-digit number that can be written using the digits 6,2,7,4,36, 2, 7, 4, 3 each only once.

Solution:

Greatest number = 76,43276,432. Least number = 23,46723,467. Difference calculation:

Explanation:

76432−2346752965\begin{array}{r} 76432 \\ -23467 \\ \hline 52965 \end{array} The difference is 52,96552,965.