krit.club logo

Large Numbers Around Us - Did You Ever Wonder…?

Grade 7CBSE

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

🔑Concepts

•

Large numbers are used to measure populations, distances between planets, and national budgets. The two primary systems are the Indian System and the International System of Numeration.

•

In the Indian System, we use periods like Units, Thousands, Lakhs, and Crores. The first comma comes after three digits from the right, and subsequent commas come after every two digits, e.g., 7,34,56,7897,34,56,789.

•

In the International System, we use periods like Units, Thousands, Millions, and Billions. Commas are placed after every three digits from the right, e.g., 73,456,78973,456,789.

•

To compare large numbers, first check the number of digits. If the number of digits is the same, compare the digits starting from the leftmost place.

•

Estimation or rounding off is used to get a quick idea of a large quantity. To round off to the nearest thousand, we look at the digit in the hundreds place. If it is 55 or more, we round up; otherwise, we round down.

📐Formulae

1 lakh=100,000=1051 \text{ lakh} = 100,000 = 10^5

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

1 crore=100 lakhs=10,000,000=1071 \text{ crore} = 100 \text{ lakhs} = 10,000,000 = 10^7

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

1 million=10 lakhs1 \text{ million} = 10 \text{ lakhs}

💡Examples

Problem 1:

Write the number 87,59,57,62187,59,57,621 in the International System and place the commas correctly.

Solution:

875,957,621875,957,621

Explanation:

In the International System, commas are placed after every three digits from the right. The number is read as Eight hundred seventy-five million, nine hundred fifty-seven thousand, six hundred twenty-one.

Problem 2:

Calculate the difference between 9,00,00,0009,00,00,000 and 4,56,78,2344,56,78,234 using vertical subtraction.

Solution:

90000000−4567823444321766\begin{array}{r} 90000000 \\ - 45678234 \\ \hline 44321766 \end{array}

Explanation:

By aligning the digits according to their place values and performing subtraction with regrouping, we find the difference is 4,43,21,7664,43,21,766.

Problem 3:

The cost of a luxury apartment is Rs 7,54,32,1007,54,32,100. Round this cost to the nearest lakh.

Solution:

Rs 7,54,00,0007,54,00,000

Explanation:

To round to the nearest lakh, we look at the ten-thousands place. The digit in the ten-thousands place is 33, which is less than 55. Therefore, we keep the lakh digit (44) as it is and change all digits to its right to zero.