In the final answer of the expression `((29.2-20.2)(1.79xx10^(5)))/1.37`. The number of significant figures is

Options

A. (a)`1 `
B. (b)`2 `
C. (c )`3 `
D. (d)` 4`

Explanation

To determine the number of significant figures in the final answer of the expression \(\frac{(29.2 - 20.2)(1.79 \times 10^5)}{1.37}\), we will follow these steps:

### Step 1: Perform the subtraction
First, we need to subtract \(20.2\) from \(29.2\):
\[ 29.2 - 20.2 = 9.0 \]
**Significant Figures in 9.0**: The number \(9.0\) has **2 significant figures** (the zero after the decimal point counts as significant).

### Step 2: Identify significant figures in the other numbers
Next, we look at the other numbers involved in the expression:
- \(1.79 \times 10^5\): The number \(1.79\) has **3 significant figures**.
- \(1.37\): The number \(1.37\) has **3 significant figures**.

### Step 3: Combine the results
Now we can rewrite the expression with the results from Step 1:
\[ \frac{(9.0)(1.79 \times 10^5)}{1.37} \]

### Step 4: Perform the multiplication
Now we multiply \(9.0\) and \(1.79\):
\[ 9.0 \times 1.79 = 16.11 \]
**Significant Figures in 16.11**: The result \(16.11\) has **4 significant figures**. However, we must consider the least precise term, which is \(9.0\) with **2 significant figures**.

### Step 5: Perform the division
Now we divide \(16.11\) by \(1.37\):
\[ \frac{16.11}{1.37} \approx 11.75 \]
**Significant Figures in 11.75**: The result \(11.75\) has **4 significant figures**. Again, we must consider the least precise term, which is \(9.0\) with **2 significant figures**.

### Step 6: Round the final answer
Since the least precise term has 2 significant figures, we round \(11.75\) to 2 significant figures:
\[ 11.75 \rightarrow 1.1 \times 10^1 \]
The final answer in scientific notation is \(1.1 \times 10^6\).

### Final Answer
Thus, the final answer has **2 significant figures**.