Place value comparison of numbers having the same number of digits.

Rohan was playing a very interesting game with his friends.

They were playing a game involving numbers.

Each of them picked up a number from $1$, $2$, $3$ and $4$.

Now, they wanted to make a $4$ digit number using these $4$ digits.

The person who made the greatest number would win the game and the one who made the smallest number would lose.

These were the numbers made by them.

Now, we have to find out who would win the game or the one who made the greatest number.

Let's look at how a number will be considered the greatest.

We know that all the numbers above are four-digit numbers.

Now, if the digit at the thousandth place is the greatest, then that number is the greatest.

Here, in $4321$, the digit at the thousandth place is the greatest. So, this is the greatest number.

Now, we have to find the smallest number of this set.

If the digit at the thousandth place is the smallest, then that number is the smallest.

Here, $1234$ is the smallest number.

So, we see that if the digit at the thousandth place is the greatest, then the number formed is the greatest. If the digit at the thousandth place is the smallest, then that number is the smallest.

This case is represented above.

Now, suppose we have numbers $627$,$567$ and $685$. We are asked to find the greatest and the smallest number.

Here the number of digits is $3$. So, we will check for the digit at the hundredth place.

We can see that 2 numbers have the greatest digit $6$.

So, we will check for the digit at the tens place & here $8$ is greatest and hence $685$ is largest number.

Now, the smallest digit at the hundredth place is $5$ and hence $567$ is the smallest number.

This way, we've found the largest and the smallest number from the set.

Revision

If two numbers have the same number of digits, the number with the bigger digit on the left-hand side is greater.

If the leftmost digits are the same, then we compare the next digit to the right and keep doing this until the digits are different.

If two numbers have the same number of digits, the number with the smallest digit on the left-hand side is the smallest.

If the leftmost digits are the same, then we compare the next digit to the right and keep doing this until the digits are different.