Question

Write the smallest and the largest six-digit numbers. How many numbers are between these two?

Answer 1

Hint: In the given question, we have been asked to write the smallest as well as the biggest six-digit number. Then, we have been asked to tell how many numbers there are in between the two six-digit numbers. To solve questions of such kind, we must know the formula of calculating the number of numbers between two numbers when either, none or both of the extreme point numbers are included.

Complete step-by-step answer:
We have to find the number of numbers between the smallest and the largest six-digit numbers. This means that neither the smallest nor the largest number is included in that.
Let us take the case when we do not remember the formula.
We are going to take a small example and then try to craft the formula from there. We are going to take the case pertaining to the question – neither of the end point numbers is included.
Let us take the example of finding the number of numbers between 1 and 15.
The numbers are – \[2,3,4,5,6,7,8,9,10,11,12,13,14\] and the number of numbers is \[13\].
So, if we have been given to find how many numbers there are between \[a\] and \[b\], then it is given by:
Number of numbers \[ = \left( {b - a} \right) - 1\]
In this question, \[a = 100000\] and \[b = 999999\]
So, the number of numbers \[ = \left( {999999 - 100000} \right) - 1 = 899999 - 1 = 899998\]
Hence, there are \[899998\] numbers between the smallest and the largest six-digit number.

Note: Here we figured out the formula by using a smaller case and then crafting a general formula. But, if we know the direct formula, then we directly apply the formula and solve for the given values.