The correctly reported answer of the addition of `29*4406, 3*2` and `2*25` will have significant figures

Options

A. Three
B. Four
C. Two
D. Five

Explanation

To determine the correctly reported answer of the addition of the numbers \(29.4406\), \(3.2\), and \(2.25\) with the appropriate significant figures, we will follow these steps:

### Step 1: Add the Numbers
First, we need to add the three numbers together.

\[ 29.4406 + 3.2 + 2.25 \]

Aligning the numbers for addition:

```
29.4406
+ 3.2000
+ 2.2500
-----------
```

Now, performing the addition:

- Start from the rightmost side:
- \(6 + 0 + 0 = 6\)
- \(0 + 0 + 0 = 0\)
- \(4 + 2 + 5 = 11\) (write down 1 and carry over 1)
- \(9 + 3 + 2 + 1 = 15\) (write down 5 and carry over 1)
- \(2 + 0 + 0 + 1 = 3\)
- \(2 + 0 + 0 = 2\)

So, the total is:

\[ 34.8906 \]

### Step 2: Determine the Number of Decimal Places
Next, we need to determine how many decimal places to keep based on the numbers we added:

- \(29.4406\) has **4 decimal places**.
- \(3.2\) has **1 decimal place**.
- \(2.25\) has **2 decimal places**.

The rule for addition is that the result should be reported to the least number of decimal places present in any of the numbers being added. Here, the number with the least decimal places is \(3.2\) with **1 decimal place**.

### Step 3: Round the Result
Now, we round \(34.8906\) to **1 decimal place**:

- The first decimal place is \(8\) and the second decimal place is \(9\).
- Since \(9\) (the second decimal place) is greater than \(5\), we round up the \(8\) to \(9\).

Thus, the rounded result is:

\[ 34.9 \]

### Step 4: Count Significant Figures
Finally, we count the significant figures in the final result \(34.9\):

- The digits \(3\), \(4\), and \(9\) are all significant.
- Therefore, there are **3 significant figures** in \(34.9\).

### Final Answer
The correctly reported answer of the addition of \(29.4406\), \(3.2\), and \(2.25\) will have **3 significant figures**.

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