Question

Find the smallest four digit number using the digits 1, 2, 5, 0 without repetition.

Answer 1

Hint: We will first arrange the given numbers in an ascending order, then we will form the smallest four digit number with the help of the obtained arranged ascending number sequence. It is to be noted that at the ten thousands place, we cannot place zero as the number will become a three digit number and we require a four digit number.

Complete step-by-step solution -
It is given in the question that we have to find the smallest four digit number using the digits 1, 2, 5, 0 without repetition. We will first arrange the given numbers in an ascending order, so we get,
0 < 1 < 2 < 5
So, the smallest number that can be formed using the digits 0, 1, 2 and 5 will be 125. But, we can see that 125 is a three digit number and we have been asked to find a four digit number. So, the smallest four digit number cannot be 125.
Now, if we interchange the place of 0 and 1, we get,
1025, which is a four digit number. Also, we can see that 1025 is the smallest four digit possible.
Hence, 1025 is the smallest four digit number that can be formed using the digits 1, 2, 5, 0.

Note: The most possible mistake that the students can make in this question is by writing 0125 as the smallest four digit number. But this is wrong, because if we place 0 in the ten thousands place, then the obtained number, that is, 125 will be a three digit number and not a four digit number as, when we place 0 before a number, that 0 has no value. For example, we can write 1 as 01, but we know that 01 is the same as 1 and it is a single digit number and not a two digit number.