What Have We Discussed ?

1. When comparing two numbers, the one with moreless digits is larger. If the number of digits in both numbers is the same, the number with the greatersmaller leftmost digit is larger. If the leftmost digits are also the same, we compare the nextprevious digit on the left and so on.

2. When forming numbers from a set of digits, make sure the conditions for making the number are satisfied. For example, to form the largest four-digit number using 6, 1, 9, 4 without repeating any digit, we arrange them in descending order: . The leftmost digit must be the largestsmallest, which in this case is .

3. The smallest four-digit number is . It follows the largest three-digit number i.e. . Similarly, the smallest five-digit number is , which follows the largest four-digit number i.e . Likewise, the smallest six-digit number is , following the largest five-digit number i.e. . This pattern continues for numbers with more digits.

4. Using commas makes reading and writing large numbers easier. In the Indian numbering system, commas are placed after every digits from the rightleft and then every digits. For example, 12,45,678 is read as twelve lakh forty-five thousand six hundred seventy-eight. In the International numbering system, commas are placed after every digits from the , such as 1,245,678, which is read as one million two hundred forty-five thousand six hundred seventy-eight.

5. Large numbers are essential in various aspects of daily life. For instance, estimating the number of students in a city, the population of a village (or) town, transactions involving large sums of money (or) measuring distances between major cities.

6. Remember that kilo means , centi means one-hundredththousandthtenth, and milli means one-thousandthtenthousandth. For example, 1 kilometer = meters, and 1 meter = centimeters or millimeters.

7. In some cases, exact numbers are unnecessary and an estimate is sufficient. For example, if reporting the attendance of an international cricket match, we might approximate it to 48,000 rather than stating the exact number.

8. Estimation means approximating a number to the required accuracy. For example, 5,243 can be rounded to 5,200 or 5,000, depending on whether we round to the nearest hundred or thousand.

9. In many situations, we estimate the outcome of arithmetic operations by rounding numbers and making quick calculations. This helps to save time and ensure accuracy.

10. Numbers are used in both the Indo-Arabic system and the International system, each with distinct ways of representing large numbers.