Question

The smallest 4-digit number formed by using the digits 5, 0, 3, 1, 7 only once contains:
A. 0 in thousand’s place
B. 5 in ten’s place
C. 3 in ten’s place
D. 7 in ten’s place

Answer 1

Hint: We form a four-digit number that has the smallest value from all other four-digit numbers. We place any number except the digit 0 in the thousands place and then proceed to fill out hundreds, tens and ones place in increasing order of the given digits. Since digits cannot be repeated we remove the assigned digit for choice of digits for the next position.
* A four digit number is a number that has elements in four places i.e. digits from 1 to 9 in thousands place and digits from 0 to 9 in ones, tens and hundreds place.

Complete step-by-step solution:
We have five digits 5, 0, 3, 1 and 7
Since we have to form a four digit number we will have to fill out four places using these digits.
Digit at thousand’s place:
Since we have to form the smallest four digit number we will choose the smallest digit from 5, 0, 3, 1 and 7.
Smallest digit is 0 but we cannot choose 0 for this position as then the number formed will be a three-digit number which contradicts our requirement of a four-digit number.
Next smallest digit is 1.
\[ \Rightarrow \]Digit at thousand’s place is 1………………..… (1)
Digit at hundreds place:
Now we are left with options for the position as 0, 3, 5 and 7
The smallest digit from the given digits is 0.
\[ \Rightarrow \]Digit at hundred’s place is 0………………….… (2)
Digit at ten’s place:
Now we are left with options for the position as 3, 5 and 7
The smallest digit from the given digits is 3.
\[ \Rightarrow \]Digit at ten’s place is 3……………...… (3)
Digit at one’s place:
Now we are left with options for the position as 5 and 7
The smallest digit from the given digits is 5.
\[ \Rightarrow \]Digit at one’s place is 5…………...… (4)
From equations (1), (2), (3) and (4) we can write the number formed is 1035
Since we have the number 1035, we can write digits lying at which place as we have options to choose from similar criteria.
1 is in a thousand's place, 0 is in hundreds places, 3 is in ten’s place and 5 is in one’s place.
\[\therefore \]The smallest 4-digit number is 1035 and 3 is in ten’s place is the matching option.

\[\therefore \]Option C is the correct answer.

Note: Many students make the mistake of beginning the 4-digit number using the digit 0 which is wrong as then the number will become a 3-digit number as 0 placed in starting will not give any value to the number. Keep in mind 0 is not to be considered for thousand’s places but it has to be considered for the next place.