Question

show the calculator answer, significant digits answer and identify the number of significant digits. show all work.
98 x 0.006=

make it more clear.

Answer 1

Let's calculate the product of \( 98 \) and \( 0.006 \) while considering significant digits.

### Step 1: Perform the Calculation

Using a calculator:

\[
98 \times 0.006 = 0.588
\]

### Step 2: Determine Significant Digits

**Definition of Significant Digits:**
- All non-zero digits are significant.
- Any zeros between significant digits are significant.
- Leading zeros (zeros before the first non-zero digit) are not significant.
- Trailing zeros in a decimal number are significant.

#### Analyzing the Numbers:

1. **For 98:**
- It has **2 significant digits** (9 and 8).

2. **For 0.006:**
- The non-zero digit is 6. The leading zeros (0.00) are not significant.
- It has **1 significant digit** (the 6).

### 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 factor with the least number of significant digits.

- The number with the least significant digits is \( 0.006 \) with **1 significant digit**.

### Step 4: Final Result with Correct Significant Digits

We calculated the result as \( 0.588 \), but we need to round this to **1 significant digit**.

- The rounded number with **1 significant digit** will be \( 0.6 \).

### Final Answers

- **Calculator answer:** \( 0.588 \)
- **Significant digits answer:** \( 0.6 \)
- **Number of significant digits in the final answer:** **1 significant digit**

This process shows how we ensure the final answer respects significant digit rules in multiplication.