Evaluae:` 4.236 xx 2.4`

Options

A. `10.1884 `
B. `10.1654 `
C. `10.1664 `
D. `10.1698 `

Answer

To evaluate \( 4.236 \times 2.4 \), we can follow these steps:

### Step 1: Convert the decimals to whole numbers
We can rewrite \( 4.236 \) as \( 4236 \) (by multiplying by 1000) and \( 2.4 \) as \( 24 \) (by multiplying by 10).

### Step 2: Multiply the whole numbers
Now we will multiply \( 4236 \) by \( 24 \).

\[ 4236 \times 24 \]

### Step 3: Perform the multiplication
1. Multiply \( 4 \) (from \( 24 \)) by \( 4236 \):
- \( 4 \times 6 = 24 \) (write down 4, carry over 2)
- \( 4 \times 3 = 12 + 2 = 14 \) (write down 4, carry over 1)
- \( 4 \times 2 = 8 + 1 = 9 \) (write down 9)
- \( 4 \times 4 = 16 \) (write down 16)

So, the first row of multiplication gives us \( 16944 \).

2. Now, multiply \( 2 \) (from \( 24 \)) by \( 4236 \) and shift one position to the left:
- \( 2 \times 6 = 12 \) (write down 2, carry over 1)
- \( 2 \times 3 = 6 + 1 = 7 \) (write down 7)
- \( 2 \times 2 = 4 \) (write down 4)
- \( 2 \times 4 = 8 \) (write down 8)

So, the second row of multiplication gives us \( 8472 \).

### Step 4: Add the results
Now we add \( 16944 \) and \( 8472 \):

```
16944
+ 8472
-------
101424
```

### Step 5: Place the decimal point
Now we need to account for the decimal places. In \( 4.236 \), there are 3 decimal places, and in \( 2.4 \), there is 1 decimal place. So, we have a total of \( 3 + 1 = 4 \) decimal places.

Thus, we place the decimal point in \( 101424 \) to get \( 10.1424 \).

### Final Answer
The final answer is:

\[ \boxed{10.1424} \]

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