Question

show the calculator answer, significant digits answer and identify the number of significant digits. show all work.
23.4 x 14

make it more clear.

Answer 1

Let's solve the problem step by step.

### Problem Statement
Calculate \(23.4 \times 14\).

### Step 1: Calculator Answer
First, perform the multiplication using a calculator:

\[
23.4 \times 14 = 327.6
\]

### Step 2: Significant Digits
Next, we need to determine the number of significant digits in each of the numbers involved in the multiplication.

- **For 23.4**:
- This number has **3 significant digits** (the digits 2, 3, and 4).

- **For 14**:
- This number has **2 significant digits** (the digits 1 and 4).

### Step 3: Applying Significant Figures Rule
When multiplying numbers, the result should be reported with the same number of significant digits as the factor with the fewest significant digits.

- Here, 23.4 has 3 significant digits.
- 14 has 2 significant digits.

Since 14 has the fewest significant digits (2), the final answer must be rounded to **2 significant digits**.

### Step 4: Rounding the Calculator Answer
The calculator answer is \(327.6\). We need to round this to 2 significant digits:

- The first two significant digits are **3** and **2**.
- Looking at the next digit (7), it indicates we should round up.

Therefore, \(327.6\) rounded to 2 significant digits is \(33\).

### Final Answer
1. **Calculator Answer**: \(327.6\)
2. **Significant Digits Answer**: \(33\)
3. **Number of Significant Digits**: \(2\)

### Summary
- The original multiplication yields \(327.6\).
- Rounding to the appropriate significant digits gives us \(33\).