` 23.003 xx 22.998 + 100.010` = ?

Options

A. 630
B. 550
C. 700
D. 720

Answer

To solve the expression \( 23.003 \times 22.998 + 100.010 \) using approximation, we can follow these steps:

### Step 1: Approximate the numbers
- **Approximate \( 23.003 \)**: Since \( 23.003 \) is very close to \( 23 \), we can approximate it as \( 23 \).
- **Approximate \( 22.998 \)**: Since \( 22.998 \) is very close to \( 23 \) but slightly less, we can also approximate it as \( 23 \).
- **Approximate \( 100.010 \)**: Since \( 100.010 \) is very close to \( 100 \), we can approximate it as \( 100 \).

### Step 2: Rewrite the expression with approximations
Now, we can rewrite the expression using our approximations:
\[ 23.003 \times 22.998 + 100.010 \approx 23 \times 23 + 100 \]

### Step 3: Calculate the multiplication
Next, we calculate \( 23 \times 23 \):
\[ 23 \times 23 = 529 \]

### Step 4: Add the approximated values
Now, we add \( 529 \) and \( 100 \):
\[ 529 + 100 = 629 \]

### Step 5: Final approximation
Since we approximated the numbers, our final result \( 629 \) is very close to the actual value. Rounding this to the nearest whole number gives us:
\[ \approx 630 \]

### Final Result
Thus, the approximate value of the expression \( 23.003 \times 22.998 + 100.010 \) is \( 630 \).

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