Page 17 - Start Up Mathematics_5

Example 9: Which is greater—2,03,544 or 43,809?

Solution: Since 2,03,544 has 6 digits while 43,809 has 5 digits, 2,03,544 > 43,809.

Example 10: Use the shortcut method to compare P P P P P 
6,23,73,478 and 6,23,73,748. 6 2 3 7 3 4 7 8
6 2 3 7 3 7 4 8
Solution: Since 4 < 7; 6,23,73,478 < 6,23,73,748

Example 11: Arrange the following numbers in ascending and descending order.

8,06,13,408 83,43,999 13,00,55,444 7,89,21,036

Solution: • 83,43,999 has the least number of digits. Thus, it is the smallest number.
• 13,00,55,444 has the maximum number of digits. Thus, it is the biggest
number.

• As 8,06,13,408 and 7,89,21,036 have the 
same number of digits, let’s compare 8 0 6 1 3 4 0 8
them. 7 8 9 2 1 0 3 6
Since 8 > 7; 8,06,13,408 > 7,89,21,036
The numbers when arranged in the descending order are,

13,00,55,444 > 8,06,13,408 > 7,89,21,036 > 83,43,999
The numbers when arranged in the ascending order are,

83,43,999 < 7,89,21,036 < 8,06,13,408 < 13,00,55,444

Juggling with Numbers

Look at the given digits. Using each one of them, we can form many 5-digit numbers by
arranging them in different order.

23,567; 23,576; 23,657; 23,675; 23,756; 23,765; 25,367; 25,637; 2
25,673; 25,736; 25,763; 26,357; 26,375; 26,537; 26,573; 26,735;
26,753; 27,356; 27,365; 27,536; 27,563; 27,635; 27,653; ... 6 7
(120 numbers)
The smallest 5-digit number formed by the digits 2, 3, 5, 6 and 3 5
7 is 23,567 and the largest 5-digit number formed is 76,532.

Example 12: Using the digits 4, 6, 9, 0, 1, 2 and 8 only once, form the largest and the
smallest possible number of 7-digits.

Solution: The largest possible number is obtained by arranging the digits in
the descending order which gives us 9864210.
The smallest possible number is obtained by arranging the digits in the
ascending order. However, we cannot begin with zero as this will give us a
6-digit number. Thus, the required number is 1024689.

9