Question

show the calculator answer, significant digits answer and identify the number of significant digits. show all work.
0.00036 x 0.02

make it more clear.

Answer 1

To multiply two numbers and express the answer with the correct number of significant digits, let's follow these steps for the calculation:

1. **Calculator Calculation**:
Perform the multiplication using a calculator:
\[
0.00036 \times 0.02 = 0.0000072
\]

2. **Determining Significant Digits**:
Next, we need to identify the number of significant digits in each number:
- For **0.00036**: The leading zeros are not significant. The significant digits are "36", which gives us **2 significant digits**.
- For **0.02**: The leading zero is not significant. The significant digit is "2", which gives us **1 significant digit**.

3. **Identifying the Limiting Factor**:
According to the rules of significant digits, the result of a multiplication should have the same number of significant digits as the factor with the least significant digits. In this case, **0.02** has the least at **1 significant digit**.

4. **Rounding the Result**:
The calculator gives us \(0.0000072\), but since we need to express our answer with **1 significant digit**, we round \(0.0000072\):
- The first significant digit is "7".
- Keeping only **1 significant digit**, we can express our answer as \(0.000007\), since \(0.000007\) reflects the number rounded to the appropriate significant digits place.

5. **Final Answer**:
So, the final answer is:
\[
0.000007
\]
- **Calculated Answer**: \(0.0000072\)
- **Significant Digits Answer**: \(0.000007\)
- **Number of Significant Digits**: **1**

This clearly outlines the process of multiplication, identifying significant figures, rounding the answer, and presenting the final result.