Question

The difference between the largest 5 digit number and smallest 5 digit number is
\[\begin{align}
  & A.90000 \\
 & B.89999 \\
 & C.109999 \\
 & \text{D}.\text{None} \\
\end{align}\]

Answer 1

Hint: In this question, we need to find the difference between the largest 5 digit number and the smallest 5 digit number. For this, we will first find the largest 5 digit number using the biggest single digit (9) and then we will find the smallest 5 digit number. At last, we will make difference between them to find our required answer. For the smallest 5 digit number, we will use smaller two digits that are 0 and 1.

Complete step by step answer:
Here, we need to find the difference between the largest 5 digit number and the smallest 5 digit number.
Let us first find the largest 5 digit number.
As we know, 9 is the largest digit, so let us try to place 9 at all five places of the five-digit number we get the number as 99999. Now if we add 1 to it, the number becomes 100000 which is a six-digit number but we require the largest 5 digit number only. So 99999 is the largest 5 digit number.
Now, let us find the smallest 5 digit number.
We know, the smallest digit is 0. Placing 0 in all 5 places will give us a single-digit number only, so we need to place the second-lowest digit in the ten thousand places i.e. 1. So our number becomes 10000. Subtracting 1, we will get 9999 but it is a four-digit number. Therefore 10000 is the smallest 5 digit number.
Let us take difference between them i.e. 99999-10000
 $ \begin{align}
  & 099999 \\
 & -10000 \\
 & 0\overline{89999} \\
\end{align} $ .
So the required difference between the largest 5 digit number and the smallest 5 digit number is 89999.
Hence option B is the correct answer.

Note:
While calculating the difference between two numbers, make sure to subtract the smaller numbers from the bigger numbers. Do not write 00000 as the smallest 5 digit number, it is wrong. Students should check their answer by subtracting 1 from the smallest number and adding 1 to the largest number to find if it still is a 5 digit number or the number of digits has changed.