 Hello and welcome to the session. In this session we will learn about comparing numbers. Now consider three numbers 82, 522,589. Now we have to check that which number is the greatest and which is the smallest among these three numbers. Five is we will check the number of digits in these numbers. Now in 85 the number of digits are in 563 there are three but in this number there are five digits. Now where the number with the maximum number of digits is the greatest and 89 is the greatest number among these three numbers having 9 is the smallest number among these three numbers in 82. First compare the digits at the highest place the thousandth place the digits at the thousandth place. Now in both the numbers now in the first number 9 is greater than 6 that is the digits at the hundredth place in the first number. Therefore greater than 82 is the greater number so the smallest numbers are usually. Now among these four digits the greatest digit is 9 then the next greatest digit is 7 then after this 4 and lastly 1. It is 9 then 7 then 4 and then 1. So from finally the greatest number it will point the greatest digit then the next at the thousandth place which is that none of the digits is repeated from 700 and 5. Now let us the smallest number at none of the digits is repeated. Now among these four digits 1 then the next it is 1 then the next three digit is then the next is 7 and the last is 9. So by using these four digits such that none of the digits is repeated that will point the digit which is from these at the thousandth place. Then the next at the hundredth place is equal to the ascending and descending order. The ascending order for the smallest do the greatest arrangement and the greatest. Now let us see the example of these numbers in the ascending and descending order. Which of these numbers in the ascending order is the arrangement from the smallest to the greatest. Now the smallest number is 71 then the next smallest number is 847 then the last two greatest. So it will be 571 then 847 then 8320 then 9754. Now we will arrange these numbers in the descending order. Now the descending order is the arrangement from the greatest to the smallest. The smallest number is 9754 and the next greatest number is 8320. The next is 847 and so the descending order 9754, 8320, 847. The smallest digit number is plus 1 is equal to the smallest two digit number which is 3 digit number which is 99 plus 1 is equal to the smallest three digit number which is the greatest three digit number which is 999 plus 1 is equal to the smallest four digit number which is 1000. Now the greatest 5 digit number which is 99999 plus 1 is equal to the smallest 6 digit number Now the greatest 6 digit number which is 99999 plus 1 is equal to the smallest 7 digit number Now the greatest 7 digit number which is 9999999 plus 1 is equal to the smallest 8 digit number of new relation Now let us see how to expand. Now consider a number 117 Now here so it will be 5 into 1000 so it will be 9 into 100 plus 1 is at the 10 space so it will be 1 into 10 is at the 1 space so it will be 7 into 1 So this is how we can expand a given number. Now let us see this place soluble Now in the integer system of new relation we have once. Now consider a number we will put 2 at the 1 space, 10 space, 3 at the 100 space So this number is we can write this number as 3 digits and then we have learnt about comparing numbers, attending and descending orders, expansion of a number and system of new relation