Place Value of Digits

If the positions of the digits 3 and 8 in the number 3,187 are reversed, how much greater is the resulting number?

Incorrect. [[snippet]] Changing the 8 in the tens place to a 3 results in a change of 50, but that isn't the only change that occurs.

Great! In order to gauge how much greater the second version of the number will be than the first, just write the two numbers and subtract the smaller from the larger. The first version of the number is 3,187. When the positions of the 3 and 8 are switched, the number becomes 8,137. $$\displaystyle 8,137 - 3,187 = 4,950$$ Therefore, the number has increased by 4,950. This should make sense in terms of each individual change as well. Changing the digit in the thousands place from 3 to 8 increases the value of the number by 5,000. Changing the digit in the tens place from 8 to 3 decreases the value of the number by 50. These two changes together increase the value of the number by $$\displaystyle 5,000 + (-50) = 4,950$$.

Incorrect. [[snippet]] Changing the digit in the thousands place from 3 to 8 increases the value of the number by 5,000, but the change in the tens place must also be considered.

Incorrect. [[snippet]] The change in the thousands place is an increase (from 3 to 8), but the change in the tens place is a decrease in value (from 8 to 3). The two versions of the number do not differ by such a large difference as 5,050.

50

4,950

5,000

5,050