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