To solve the subtraction problem \(27.68 - 14.369\), we will adhere to the rules of significant figures.
Step 1: Perform the Calculation
First, we can perform the subtraction using a calculator:
\[ 27.68 - 14.369 = 13.311 \]
Step 2: Identify Significant Figures
Now we need to consider significant figures for the numbers involved in the calculation:
- 27.68 has 4 significant figures (the digits 2, 7, 6, and 8 are all significant)
- 14.369 has 5 significant figures (the digits 1, 4, 3, 6, and 9 are all significant)
Step 3: Determine the Limit for Significant Digits
When performing subtraction (or addition), the result should be reported to the least precise decimal place.
- 27.68 goes to the hundredths place (2 decimal places),
- 14.369 goes to the thousandths place (3 decimal places).
Since 27.68 is the less precise number (it has fewer decimal places), we will round the answer to match the precision of 27.68.
Step 4: Round the Result
The result of the subtraction we calculated is:
\[ 13.311 \]
We need to round \(13.311\) to 2 decimal places (to match the precision of \(27.68\)):
\[ 13.311 \approx 13.31 \]
Conclusion
So, the final result with appropriate significant digits is:
- Calculator Answer: \(13.311\)
- Rounded Significant Digits Answer: \(13.31\)
- Number of Significant Digits in the Final Answer: 4 significant digits (1, 3, 3, and 1 in \(13.31\)).
Therefore, the final answer is \(13.31\).