Forming the largest and the smallest number

Example 1

What is the largest number possible that can be formed using the digits given below if each digit is to be used once: 1, 4, 2, 7, 3

Solution

Start with the largest digit and end with the smallest 74321.

74321 in words is seventy four thousand three hundred and twenty one.

Example 2

What is the largest and the smallest numbers that can be made using the digits 1,4,0,9,8? If each digit is to be used once.

Solution

Largest number is 98410 and in words it is ninety eight thousand four hundred and ten.

Smallest number is 10489 and in words it is ten thousand, four hundred and eighty nine.

Note 

When forming the smallest number where a zero (0) is involved, we shift the zero (0) in between the first two digits and not placing it at the beginning i.e. 01489.

This is wrong because 01489 and 1489 have the same values yet in 01489 all digits in question are involved while in 1489, one digit is left out i.e. (0).

Hence the smallest number possible formed from 1,4,0,9,8 is 10489.

Form the greatest and the smallest number using the digits 6, 3, 8, 7, 1

We may say the procedure of forming the greatest number is as follows: 

1. The smallest digit is placed at one’s place. 
2. The next greater digit is placed at ten's place. 
3. The next greater digit is placed at hundred's place and so on. 
4. The greatest digit is placed at the highest place of the number. 

The smallest number is formed by the following the reverse procedure.

1. The greatest digit is placed at one's place. 
2. The next smaller digit at ten’s place and so on till all the given digits are finished. 
3. The smallest digit is placed at the highest place of the number. 

Solution

Write the greatest and smallest number with the given 5 digits (3,1,,6,8,7, ) without repeating any digit. 

Solution

                          Tth      Th     H       T       O
Greatest number    8       7       6       3       1     So, greatest number = 87631

Smallest number    1       3       6       7       8     So, smallest number = 13678 

Write the greatest 4 digit number using the digit 7 5 2 8.

Using the same digits, write the smallest number. 

To get the greatest number, we arrange the digits in descending order.

8 > 7 > 5 > 2.

The greatest number using the digits 7 5 2 8 is 8752. 

To get the smallest number, we arrange the digits in ascending order. 

2 < 5 < 7 < 8.

The smallest number using the digits 7 5 2 8 is 2578.

Write the greatest 5 digit number using 1 2 5. The digit may be repeated. 

Arrange in descending order. 5 > 2 > 1

Since we have to make the greatest 5 digit number using 3 digits, we will repeat the greatest digit required number of times. 

The greatest 5 digit number is 55521.