Perform the indicated operations assuming all numbers are approximate. The answer should be rounded using the following procedure. Keep all digits in the intermediate​ steps, but keep track of​ (perhaps by​ underlining) the significant digits that would be retained according to the appropriate rounding rule for each step. Then round off the final answer according to the last operation that is performed.

StartFraction 27.258 left parenthesis 0.01672 right parenthesis Over 8.154 minus 6.531 EndFraction

To solve the expression:

\[
\frac{27.258 \times 0.01672}{8.154 - 6.531}
\]

we will perform each step carefully, tracking and underlining significant digits as instructed.

### Step 1: Subtraction in the Denominator
Calculate the subtraction in the denominator:

\[
8.154 - 6.531 = 1.623
\]

**Significant Digits:** 
- \(8.154\) has 4 significant digits.
- \(6.531\) has 4 significant digits.
- The result of subtraction should have 4 significant digits, so 1.623 retains all 4 significant digits.

### Step 2: Multiplication in the Numerator
Calculate the multiplication in the numerator:

\[
27.258 \times 0.01672 = 0.45570176
\]

**Significant Digits:** 
- \(27.258\) has 5 significant digits.
- \(0.01672\) has 4 significant digits.
- The result of multiplication should have 4 significant digits, so 0.45570176 is rounded to **0.4557**.

### Step 3: Division
Now, divide the result from the multiplication by the result from the subtraction:

\[
\frac{0.4557}{1.623} \approx 0.280747225
\]

**Significant Digits:** 
- The numerator \(0.4557\) has 4 significant digits.
- The denominator \(1.623\) has 4 significant digits.
- The final result should have 4 significant digits, so 0.280747225 is rounded to **0.2807**.

### Final Answer
The final answer, rounded to the appropriate number of significant digits, is:

\[
\boxed{0.2807}
\]

Would you like more details or have any questions?

Here are 5 related questions:
1. How would the result change if one of the original numbers had fewer significant digits?
2. What is the significance of the last operation when determining the final rounding?
3. How can rounding during intermediate steps affect the accuracy of the final result?
4. Can you try performing these operations using different numbers and compare results?
5. How does the choice of significant digits influence the precision of scientific calculations?

**Tip:** When performing operations with numbers of varying significant digits, always apply the rules for significant digits at each step to maintain accuracy.

Explore how to perform arithmetic operations while adhering to significant figures rules. This problem involves multiplication, subtraction, and division with careful tracking of significant digits. Suitable for high school students learning precision in scientific calculations.

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