Question

The smallest 9 digit number is:
$A.$ $900000000$
$B.$ $9$
$C.$ $100000000$
$D.$ $10000000$

Answer 1

Hint: We will find the smallest $9$ digit number using natural numbers and number line. The numbers which are on the left side of the number line are smaller and the numbers which are on the right side of the number line are greater numbers. For example in these numbers $4<5<6$, $4$ is on the left side and $6$ is on the right side.

Complete step-by-step answer:

It is given in the question that we have to find the smallest $9$ digit number. Using the number line we will find the smallest $9$ digit natural number. We know that the numbers which are in the left side of the number line are smaller and the numbers which are in the right side of the number line are greater numbers.

For example in these numbers $6<7<8$, $6$ is on the left side and $8$ is on the right side.

Among these three numbers $8$ is on the right side. Thus, $8$ is the largest number.

$\Rightarrow 6<7<8$

Now, we try to find out the smallest $9$ digit number using the number line. Before finding the smallest $9$ digit number we know the largest $8$ digit number is $99999999$.

Now, we will try to find the next number on the right side of $99999999$. So, the number which is next to the number $99999999$ is $100000000$ which is a $9$ digit number and the number next to $100000000$ is $100000001$. When we represent these three numbers on number line, we get

Also, with the help of number line, we get

$99999999<100000000<100000001$

Therefore, the smallest $9$ digit number is $100000000$

When we look over the options given in question Option$(C)$ is the correct answer.

Note: The smallest natural number is $1$ and the largest $1$ digit number is $9$. Similarly, the smallest $2$ digit number is $10$ and the largest $2$ digit number is $99$. Also, the smallest $3$ digit number is $100$ and the largest $3$ digit number is $999$ and so on... The conclusion is, the numbers starting with $1$ and ends with recurring $0$ are the smallest numbers of their group. Similarly the number starting with $9$ and ends with recurring $9$ are the largest numbers of their group.