Question

show the calculator answer, significant digits answer and identify the number of significant digits. show all work.
27.68 - 14.369

make it more clear.

Answer 1

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 \(13.31\)**.