Question

show the calculator answer, significant digits answer and identify the number of significant digits. show all work.
25.7 x 0.78 x 2.3

make it more clear.

Answer 1

To perform the multiplication \( 25.7 \times 0.78 \times 2.3 \), we'll calculate the answer step by step and determine the significant figures in the final result.

### Step 1: Calculate using a calculator

1. **Calculate \( 25.7 \times 0.78 \)**:
\[
25.7 \times 0.78 = 20.046
\]

2. **Multiply the result by \( 2.3 \)**:
\[
20.046 \times 2.3 = 46.1058
\]

### Step 2: Identify significant figures

Now, we will identify the number of significant figures in each of the original numbers:

- **25.7**: 3 significant figures (the digits 2, 5, and 7)
- **0.78**: 2 significant figures (the digits 7 and 8)
- **2.3**: 2 significant figures (the digits 2 and 3)

### Step 3: Determine the limiting factor

When multiplying numbers, the result should have the same number of significant figures as the number with the fewest significant figures.

- \( 25.7 \) has **3 significant figures**
- \( 0.78 \) has **2 significant figures** (limiting factor)
- \( 2.3 \) has **2 significant figures**

Thus, our final result will be limited to **2 significant figures**.

### Step 4: Round the answer

The calculator answer from our multiplication was **46.1058**. To round this to **2 significant figures**:

1. Look at the first two digits (46).
2. The next digit (1) indicates we do not need to round up.

Thus, rounding \( 46.1058 \) to **2 significant figures** gives us **46**.

### Final Summary:

- **Calculator answer**: \( 46.1058 \)
- **Significant digits answer**: \( 46 \)
- **Number of significant digits**: **2**

So the final answer is **46** with **2 significant figures**.