`26.823 xx 27.923 xx 4.5001 = ?`

Options

A. 3500
B. 3450
C. 3100
D. 3400

Answer

To solve the expression \( 26.823 \times 27.923 \times 4.5001 \) using approximation, we can follow these steps:

### Step 1: Round Off the Numbers
We start by rounding each number to a more manageable figure:
- \( 26.823 \) rounds to \( 27 \)
- \( 27.923 \) rounds to \( 28 \)
- \( 4.5001 \) rounds to \( 4.5 \)

### Step 2: Rewrite the Expression
Now we can rewrite the expression using the rounded values:
\[ 27 \times 28 \times 4.5 \]

### Step 3: Break Down the Multiplication
We can simplify the multiplication by breaking it down:
1. First, calculate \( 27 \times 28 \).
2. Then multiply the result by \( 4.5 \).

### Step 4: Calculate \( 27 \times 28 \)
To calculate \( 27 \times 28 \), we can use the distributive property:
\[ 27 \times 28 = 27 \times (30 - 2) = (27 \times 30) - (27 \times 2) \]
Calculating each part:
- \( 27 \times 30 = 810 \)
- \( 27 \times 2 = 54 \)

Now, subtract:
\[ 27 \times 28 = 810 - 54 = 756 \]

### Step 5: Multiply by \( 4.5 \)
Now we multiply the result by \( 4.5 \):
\[ 756 \times 4.5 \]
We can break this down further:
\[ 756 \times 4.5 = 756 \times (4 + 0.5) = (756 \times 4) + (756 \times 0.5) \]
Calculating each part:
- \( 756 \times 4 = 3024 \)
- \( 756 \times 0.5 = 378 \)

Now, add these results:
\[ 756 \times 4.5 = 3024 + 378 = 3402 \]

### Step 6: Final Approximation
The approximate result of \( 26.823 \times 27.923 \times 4.5001 \) is \( 3402 \).

### Conclusion
Thus, the final answer is approximately \( 3400 \).

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