Building (forming numbers): Greatest and the Smallest

Here’s how to form numbers using digits. Learn for to for the greatest number and the smallest number using a set of digits.

Building Numbers

But before we proceed, a recap of important points:

Greatest one digit number = 9, Smallest 2 digit number = 10.
Greatest 2 digit number = 99, Smallest 3 digit number = 100.
Greatest 3 digit number = 999, Smallest 4 digit number = 1000.
Greatest 4 digit number = 9999, Smallest 5 digit number = 10000.

Did you notice that if you add 1 to the Greatest number, you get the smallest number of a higher digit number?

So lets start with building numbers. Let us start with a simple example.

How many 2-digit numbers can be formed using the digits 2 and 7?

There are two ways to make 2-digit numbers using the given digits.

1. By repeating the digits – 22 and 77
2. Without repeating the digits – 27 and 72

So there are four 2-digit numbers that can be made using the digits 2 and 7.

You should tell your kids to pay attention to the question on forming numbers, because if the word “repeated” is mentioned in the question, it will yield a different answer.

How to Form the Greatest Number

Here’s how to build the greatest number:

1. Start with the greatest (largest) digit and put it in the place with the greatest place value
2. Pick the next greatest (largest) digit and put it in the place with the next greatest place value.
3. Repeat this until all the digits are placed

The number obtained will be the greatest number that can be formed with those digits.

For example. Consider 3-digits 6, 7 and 3.

So to form the greatest number, you start with 7 (greatest digit) and place it at the Hundredth place. You then pick 6 and place it at the Tenth place and finally place 3 at the Ones position.

So the greatest number formed is 763 using the digits 6, 7 and 3.

Note: If repetition of digits were allowed, the Greatest number would be 777.

How to Form the Smallest Number

Here’s how to form the smallest number:

1. Start with the smallest digit and put it in the place with the greatest place value
2. Pick the next smallest digit and put it in the place with the next greatest place value.
3. Repeat this until all the digits are placed

The number obtained will be the smallest number that can be formed with those digits.

For example. Again consider those 3-digits 6, 7 and 3.

So to form the smallest number, you start with 3 (smallest digit) and place it at the Hundredth place. You then pick 6 and place it at the Tenth place and finally place 7 at the Ones position.

So the greatest number formed is 367 using the digits 6, 7 and 3.

Note: If repetition of digits were allowed, the Smallest number would be 333.