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

Options

A. 1
B. 2
C. 3
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
Calculate \(29.2 - 20.2\):
\[ 29.2 - 20.2 = 9.0 \]
**Hint:** When subtracting, the result should have the same number of decimal places as the term with the least decimal places.

### Step 2: Identify significant figures in the result of the subtraction
The result \(9.0\) has **2 significant figures** (the zero after the decimal point counts).

**Hint:** Remember that trailing zeros in a decimal number are significant.

### Step 3: Identify significant figures in the other numbers
- \(1.79\) has **3 significant figures**.
- \(10^5\) does not contribute to significant figures, as it is a power of ten.
- \(1.37\) has **3 significant figures**.

**Hint:** Only the digits in the coefficient (the non-exponential part) contribute to significant figures.

### Step 4: Determine the limiting factor for significant figures
The significant figures in the calculation will be determined by the term with the least number of significant figures. Here, we have:
- Result of subtraction: **2 significant figures**
- \(1.79\): **3 significant figures**
- \(1.37\): **3 significant figures**

The term with the least significant figures is \(9.0\) from the subtraction, which has **2 significant figures**.

**Hint:** The final answer must reflect the least number of significant figures from the numbers involved in the calculation.

### Step 5: Perform the multiplication and division
Now, we calculate:
\[ \frac{(9.0)(1.79 \times 10^5)}{1.37} \]

Calculating the numerator:
\[ 9.0 \times 1.79 \approx 16.11 \]

Now divide by \(1.37\):
\[ \frac{16.11}{1.37} \approx 11.74 \]

### Step 6: Round the final answer to the correct number of significant figures
Since the limiting factor is **2 significant figures**, we round \(11.74\) to **2 significant figures**, which gives us:
\[ 1.2 \times 10^1 \text{ (or simply 12)} \]

Thus, the final answer has **2 significant figures**.

### Final Answer
The number of significant figures in the final answer of the expression is **2**.

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