Question

How many numbers are there containing three digits?

Answer 1

Hint: Here, first we should know how many numbers are used for a one digit number. They are 1, 2, 3, 4, 5, 6, 7, 8 and 9. For, a three digit number there are three places. Unit’s place, ten’s place and hundreds place. For unit’s and ten’s place we use the numbers 0 to 9 and for hundreds place we use the numbers 1 to 9. Using this we can find the number of three digit numbers.

Complete step-by-step answer:
We know that there are 9 one digit numbers. They are 1, 2, 3, 4, 5, 6, 7, 8 and 9. There are 90 two-digit numbers from 10 t0 99. One digit numbers are made by the digits 1, 2, 3, 4, 6, 7, 8 and 9. For the making of two digit numbers zero is also used along with the numbers from 1 to 9. In two digit numbers one digit represents the number of one’s or unit’s and the other represents the number of ten’s.
 Now, for a three digit number we have to start from 100 and the highest three digit number is 999. In a three digit number there are three places used- hundreds ten’s and unit’s.
Here, for the unit's place we can use the numbers 0,1, 2, 3, 4, 5, 6, 7, 8 and 9. So, there are 10 possibilities in the unit's place.
Now, for ten’s place we can use the numbers 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9. So, here also there are 10 possibilities in ten’s place.
Now, for hundred’s place we can use the numbers 1, 2, 3, 4, 5, 6, 7, 8 and 9. We can’t use zero at hundred’s place, since it will become a two digit number. Hence, for hundred’s place we have 9 possibilities.
Hence, the number of 3 digit numbers = $9\times 10\times 10$
Number of 3 digit numbers = 900
Therefore, we can say that there are 900 three digit numbers.

Note: Here for unit’s and ten’s place you can use the numbers from 0 to 9. But in hundred’s place you can’t use the number zero, since zero used in the beginning of a number has no value. If you use zero in hundred’s place it will be considered as a two digit number.