To solve the division problem \( 986.72 \div 5.12 \) and to determine the answer with significant digits, we will follow these steps:
Step 1: Perform the Calculation
Using a calculator or standard division, we compute:
\[ 986.72 \div 5.12 \approx 192.1875 \]
Step 2: Determine Significant Digits
Next, we need to consider the significant digits in our original numbers.
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For 986.72:
- This number has 5 significant digits (all non-zero digits and the decimal).
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For 5.12:
- This number has 3 significant digits (all non-zero digits).
Step 3: Apply the Rules for Significant Digits in Division
When carrying out calculations like division, the result should be reported with the same number of significant digits as the value with the fewest significant digits.
In this case, \( 5.12 \) has the fewest significant digits, which is 3 significant digits.
Step 4: Round the Result
Now we need to round our result, \( 192.1875 \), to 3 significant digits:
- The first three significant digits in \( 192.1875 \) are 192.
- The next digit (the fourth) is 1, which means we do not round up.
Thus, rounding \( 192.1875 \) to 3 significant digits gives us:
\[ 192 \]
Final Answer
Therefore, the final answer to the division \( 986.72 \div 5.12 \) with the appropriate significant digits is:
\[ \boxed{192} \]
Summary
- Calculator Answer: \( 192.1875 \)
- Significant Digits Answer: \( 192 \)
- Number of Significant Digits in the final result: \( 3 \)