`13.5 xx 16.3 xx 12.8 = ?`

Options

A. 2861.46
B. 2168.46
C. 2816.64
D. 2186.64

Answer

To solve the multiplication of the numbers 13.5, 16.3, and 12.8, we can follow these steps:

### Step 1: Remove the Decimal Points
To make the multiplication easier, we can first convert the decimal numbers into whole numbers by multiplying each by 10.

- \( 13.5 \times 10 = 135 \)
- \( 16.3 \times 10 = 163 \)
- \( 12.8 \times 10 = 128 \)

Now we need to multiply these whole numbers:
\[ 135 \times 163 \times 128 \]

### Step 2: Multiply the First Two Numbers
Let's start by multiplying the first two numbers:
\[ 135 \times 163 \]

To do this, we can use the standard multiplication method:
1. Multiply \( 135 \) by \( 3 \) (the units place of \( 163 \)):
- \( 135 \times 3 = 405 \)
2. Multiply \( 135 \) by \( 6 \) (the tens place of \( 163 \)):
- \( 135 \times 6 = 810 \) (but since it's in the tens place, we need to add a zero: \( 8100 \))
3. Multiply \( 135 \) by \( 1 \) (the hundreds place of \( 163 \)):
- \( 135 \times 1 = 13500 \)

Now, we add these results together:
\[ 405 + 8100 + 13500 = 22005 \]

So, \( 135 \times 163 = 22005 \).

### Step 3: Multiply the Result with the Third Number
Now we need to multiply the result \( 22005 \) by \( 128 \):
\[ 22005 \times 128 \]

Using the same multiplication method:
1. Multiply \( 22005 \) by \( 8 \) (the units place of \( 128 \)):
- \( 22005 \times 8 = 176040 \)
2. Multiply \( 22005 \) by \( 2 \) (the tens place of \( 128 \)):
- \( 22005 \times 2 = 44010 \) (but since it's in the tens place, we need to add a zero: \( 440100 \))
3. Multiply \( 22005 \) by \( 1 \) (the hundreds place of \( 128 \)):
- \( 22005 \times 1 = 2200500 \)

Now, we add these results together:
\[ 176040 + 440100 + 2200500 = 2817840 \]

### Step 4: Adjust for the Decimal Places
Since we initially multiplied each number by 10, we need to adjust for the three decimal places we removed (one for each of the three numbers). Therefore, we divide the final result by \( 10^3 = 1000 \):
\[ \frac{2817840}{1000} = 2817.84 \]

### Final Answer
Thus, the final answer is:
\[ 13.5 \times 16.3 \times 12.8 = 2817.84 \]

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