Question

show the calculator answer, significant digits answer and identify the number of significant digits. show all work.
400.20 x 3.010 =

make it more clear.

Answer 1

To solve the multiplication \( 400.20 \times 3.010 \) while considering significant digits, we will follow these steps:

1. **Perform the calculation using a calculator**.
2. **Identify the significant digits** in each number.
3. **Determine the result ensuring the correct number of significant digits**.

### Step 1: Calculation

Using a calculator:

\[
400.20 \times 3.010 = 1204.602
\]

### Step 2: Identifying Significant Digits

Now we will identify the significant digits for each of the numbers involved in the multiplication:

- **For \( 400.20 \)**:
- This number has 5 significant digits (the zeros after the decimal point are considered significant).

- **For \( 3.010 \)**:
- This number has 4 significant digits (the zero after the "3" and before the "1" is significant).

### Step 3: Determine the Number of Significant Digits in the Result

When multiplying numbers, the result should be reported with the same number of significant digits as the measurement with the least significant digits:

- \( 400.20 \) has **5 significant digits**.
- \( 3.010 \) has **4 significant digits**.

#### Conclusion on Significant Digits

Since \( 3.010 \) has the least number of significant digits (4), we will round our answer to **4 significant digits**.

### Rounding the Result

The calculated result was \( 1204.602 \). We need to round this to **4 significant digits**:

- The first four significant digits are **1204**.
- The next digit is a **6**, which means we round up the last significant digit (4).

Thus, rounding \( 1204.602 \) to 4 significant digits gives us:

\[
\text{Rounded Result} = 1205
\]

### Final Result

\[
\text{Final Answer} = 1205 \quad (\text{with 4 significant digits})
\]

### Summary:

- **Calculator Answer**: \( 1204.602 \)
- **Significant Digits Answer**: \( 1205 \)
- **Number of Significant Digits**: 4