Question

show the calculator answer, significant digits answer and identify the number of significant digits. show all work.
497.7 / 3.0=

make it more clear.

Answer 1

To solve the problem \(497.7 \div 3.0\) and analyze it in terms of significant digits, we will proceed with the following steps:

### Step 1: Perform the calculation

Using a calculator:
\[
497.7 \div 3.0 = 165.9
\]

### Step 2: Identify significant figures

Next, we need to determine how many significant digits are in each number involved in the calculation.

- **For 497.7**: This number has **4 significant digits**. The digits 4, 9, 7, and the decimal 7 are all significant.

- **For 3.0**: This number has **2 significant digits**. The digit 3 is significant, and the trailing zero after the decimal point (0) is also significant.

### Step 3: Apply significant digits rules

When performing division, the result should be rounded to the same number of significant digits as the measurement with the least significant digits. In this case, **3.0** has the least number of significant digits (2).

### Step 4: Rounding the result

The result of our calculation is \(165.9\). We will round this to **2 significant digits**:

- The first two digits of \(165.9\) are **16**.
- The digit immediately following the second significant digit (which is 5) indicates that we should round the number up.

Thus, rounding \(165.9\) with 2 significant digits gives us \(17\) (as \(16\) becomes \(17\) when rounded).

### Final Answer

\[
\text{So the final result, considering significant digits, is } \boxed{170}.
\]

In summary:

- **Calculator answer**: \(165.9\)
- **Significant digits answer**: \(170\)
- **Significant digits**: 2 (since we rounded the final answer to match the digits of the number with the least significant figures, which is 3.0).