What number can you subtract from 3,200 so that their differences is a 4 digit number with the digits in the thousands place,
The digits in the hundreds place and zero in the tens and ones place
What are the numbers in these places?
900
W2300
To find the number that can be subtracted from 3,200 to get a four-digit number with specific digit placements, we can follow these steps:
Step 1: Identify the digit placement requirements for the resulting number:
Given that the resulting number should have the digit in the thousands place, the digit in the hundreds place, and zero in the tens and ones place, we can represent it as follows:
_ _ _ _
_ _ _ _ (Thousand, Hundred, Tens, Ones)
Step 2: Determine the possible range of values for each digit:
Since the difference between 3,200 and the unknown number should be a four-digit number, we need to consider the minimum and maximum values for each digit placement:
- Thousands place: Ranges from 1 to 9 (as it can't be zero, as per the given requirements).
- Hundreds place: Ranges from 0 to 9 (can be any digit including zero).
- Tens place: Only zero (as per the given requirements).
- Ones place: Only zero (as per the given requirements).
Step 3: Calculate the difference between 3,200 and the unknown number:
Let's assume the unknown number to be subtracted is represented as follows:
_ _ _ _
_ _ _ _ (Thousand, Hundred, Tens, Ones)
Subtracting this number from 3,200, we get:
3,200 - (_ _ _ _ _ _) = _ _ _ _ _
Step 4: Determine the possible values for each digit:
- Thousands place: Since the difference must be in the thousands, and the known number (3,200) already has 0 in the thousands place, the difference can only have a single digit in the thousands place. Hence, the thousands place can take any value from 1 to 9.
- Hundreds place: The difference can be any digit from 0 to 9.
- Tens place: Since the given requirements specify the digit to be zero here, the tens place should only be zero.
- Ones place: Similar to the tens place, the ones place should only be zero.
Step 5: Combine the possible values for each digit placement:
Based on the above analysis, all the possible values for the difference between 3,200 and the unknown number are:
1,000
2,000
3,000
...
9,000
Therefore, any number between 1,000 and 9,000 (inclusive) can be subtracted from 3,200 to obtain a four-digit number with the digit in the thousands place, the digit in the hundreds place, and zero in the tens and ones place.