Question

Rearrange the digits of the number $2,01,53,007$ to get the largest and the smallest number. The difference in the place values of $2$ in these two numbers is

• A. $8000$
• B. $0$
• C. $18000$
• D. $180000$

Answer 1

The correct option is C

$18000$

Explanation for the correct option:

Option $C$: $18000$

The number given is $2,01,53,007$.

Step I: Finding the smallest number.

Arranging the digits of the given number in increasing order we will get the smallest number.

Also, zero cannot be placed as the first digit as zero placed before the digits have no value.

So, instead we will place $1$ as the first digit followed by $0$ and then $2$.

Therefore, the smallest number is $10002357$.

Step II: Finding the largest number.

Arranging the digits of the given number in decreasing order will give the largest number.

Therefore, the largest number is $75321000$.

Step III: Finding the place value of $2$ in the smallest and greatest number.

In the smallest number $10002357$, the digit $2$ is present at the thousands place.

Hence, the place value of $2$ is $2000$.

In the largest number $75321000$, the digit $2$ is present at the ten-thousands place.

Hence, the place value of $2$ is $20,000$.

Step IV: Finding the difference between the place values of $2$.

Difference$=20,000-2000$

$=18,000$.

Therefore, the difference in the place values of $2$ in these two numbers is $18,000$.

Hence, the correct option is option $C$.