Estimate the difference by first rounding each number to the nearest hundred.9845 - 1268 - 1412 is about

1. Break Down the Problem

We need to estimate the difference between three numbers: 9845, 1268, and 1412. To do this, we will first round each number to the nearest hundred.

2. Relevant Concepts

Rounding involves adjusting a number to the nearest specified value. The rules for rounding to the nearest hundred are as follows:

• If the tens digit is 5 or greater, round up.
• If the tens digit is less than 5, round down.

3. Analysis and Detail

1. Round each number:

   • For 9845: The tens digit is 4 (less than 5), so we round down to 9800.
   • For 1268: The tens digit is 6 (greater than or equal to 5), so we round up to 1300.
   • For 1412: The tens digit is 1 (less than 5), so we round down to 1400.

2. Set up the estimation: $9800 - 1300 - 1400$

4. Verify and Summarize

Now, we will perform the calculations:

• First, calculate $9800 - 1300$: $9800 - 1300 = 8500$
• Then, subtract $1400$: $8500 - 1400 = 7100$

Final Answer

The estimated difference is about 7100.