Let's break down the calculation of \(3.08 \times 5.2\) step-by-step, showing the calculator answer, the rules for significant digits, the final answer with the correct significant digits, and the reasoning behind it.
Step 1: Calculator Calculation
Using a calculator to perform the multiplication:
\[ 3.08 \times 5.2 = 16.016 \]
Step 2: Identifying Significant Digits
Now, we need to identify the number of significant digits in each of the numbers being multiplied.
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For 3.08:
- It has 3 significant digits (the digits '3', '0', and '8').
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For 5.2:
- It has 2 significant digits (the digits '5' and '2').
Step 3: Applying the Rule for Significant Digits
When performing multiplication, the result should have the same number of significant digits as the number in the calculation with the least number of significant digits.
In this case:
- 3.08 has 3 significant digits.
- 5.2 has 2 significant digits.
Since 5.2 has the least number of significant digits (2), the final result must also be expressed with 2 significant digits.
Step 4: Rounding the Result
The calculator result is 16.016. To round this to 2 significant digits, we look at the first two digits (1 and 6).
- The third digit is '0', which does not round up the 6.
- Therefore, we round 16.016 to 16.
Final Answer
The final answer for the multiplication \(3.08 \times 5.2\), with the correct significant digits, is:
\[ \boxed{16} \]
Summary
- Calculator Answer: 16.016
- Final Answer (with correct significant digits): 16
- Number of Significant Digits: 2 (from 5.2)