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.