Estimate: `5, 673-436` by rounding off the numbers to their greatest places (nearest hundreds). Also, find the reasonable estimate.

Options

A. `5900`
B. `5300`
C. `6000`
D. `5500`

Answer

To estimate \( 5,673 - 436 \) by rounding off the numbers to their greatest places (nearest hundreds), we will follow these steps:

### Step 1: Round off the first number (5,673) to the nearest hundred.
- The hundreds place in 5,673 is 6 (which is in the hundreds place).
- The digit to the right of 6 (which is 7) is greater than 5, so we round up.
- Therefore, \( 5,673 \) rounded to the nearest hundred is \( 5,700 \).

### Step 2: Round off the second number (436) to the nearest hundred.
- The hundreds place in 436 is 4.
- The digit to the right of 4 (which is 3) is less than 5, so we round down.
- Therefore, \( 436 \) rounded to the nearest hundred is \( 400 \).

### Step 3: Subtract the rounded numbers.
- Now we subtract the rounded numbers:
\[ 5,700 - 400 = 5,300 \]

### Conclusion:
The estimated result of \( 5,673 - 436 \) after rounding to the nearest hundreds is \( 5,300 \).

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