To solve the problem \(23.4 \times 14\) while paying attention to significant digits, follow these steps:
Step 1: Perform the calculation
Using a calculator: \[ 23.4 \times 14 = 327.6 \]
Step 2: Identify significant digits in the numbers
- 23.4 has 3 significant digits (the non-zero digits and the digit after the decimal).
- 14 has 2 significant digits (the non-zero digits).
Step 3: Determine the result with respect to significant digits
According to the rules of significant digits:
- The result should be reported based on the number with the least significant digits.
- Here, 14 has the least significant digits (2 significant digits). Therefore, the final result should also be reported with 2 significant digits.
Step 4: Round the result
The raw calculation gives \(327.6\). To round this result to 2 significant digits:
- The first two significant digits in \(327.6\) are 32. The next digit to the right is 7 (which is greater than 5), so we round up.
- Thus, rounding \(327.6\) to 2 significant digits gives us: \[ \text{Rounded result} = 33 , 0 \text{ (with respect to significant digits)} \]
Final Answer
The calculator result is: \[ 327.6 \] The significant digits answer is: \[ 33 \text{ (2 significant digits)} \]
Summary
- Calculator Result: \(327.6\)
- Significant Digits Answer: \(33\) (2 significant digits)
- Number of Significant Digits in final answer: 2
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