Number of significant figures in the answer of the following will be `((29.2-20.2)(1.79xx105))/1.39`

Options

A. 4
B. 3
C. 2
D. 1

Answer

To determine the number of significant figures in the expression \(((29.2 - 20.2)(1.79 \times 10^5))/1.39\), we will follow these steps:

### Step 1: Perform the subtraction
Calculate \(29.2 - 20.2\).

\[ 29.2 - 20.2 = 9.0 \]

**Significant Figures in this Step:**
- Both 29.2 and 20.2 have three significant figures.
- The result, 9.0, has two significant figures (the decimal point indicates that the zero is significant).

### Step 2: Identify significant figures in the multiplication
Next, we consider the multiplication of the result from Step 1 with \(1.79 \times 10^5\).

\[ (9.0)(1.79 \times 10^5) \]

**Significant Figures in this Step:**
- The number 9.0 has two significant figures.
- The number \(1.79 \times 10^5\) has three significant figures.
- When multiplying, the result will have the same number of significant figures as the term with the least significant figures, which is 9.0 (2 significant figures).

### Step 3: Perform the multiplication
Now we calculate:

\[ 9.0 \times 1.79 \times 10^5 = 16.11 \times 10^5 \]

However, we need to round this to 2 significant figures:

\[ 16.11 \times 10^5 \approx 1.6 \times 10^6 \]

### Step 4: Divide by 1.39
Now we divide the result by \(1.39\):

\[ \frac{1.6 \times 10^6}{1.39} \]

**Significant Figures in this Step:**
- The number \(1.6 \times 10^6\) has 2 significant figures.
- The number 1.39 has three significant figures.
- The result will again have 2 significant figures (the least number of significant figures from the terms involved).

### Step 5: Perform the division
Calculating the division:

\[ \frac{1.6 \times 10^6}{1.39} \approx 1.15 \times 10^6 \]

### Final Result
Since we need to express this with 2 significant figures, we round it to:

\[ 1.2 \times 10^6 \]

### Conclusion
The final answer has **2 significant figures**.

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