((2.0265-2.02)/2.0265)*100.00 with significant figures

Let's calculate \(\left(\frac{2.0265 - 2.02}{2.0265}\right) \times 100.00\) while keeping track of significant figures.

1. Subtraction: 
   \[
   2.0265 - 2.02 = 0.0065
   \]
   The result should have **2 decimal places**, since \(2.02\) has the least number of decimal places (2 significant figures after the decimal).

2. Division:
   \[
   \frac{0.0065}{2.0265} = 0.003208
   \]
   Here, the answer will be rounded to **4 significant figures**, because \(0.0065\) has 2 significant figures and \(2.0265\) has 5 significant figures. The result should follow the smaller number of significant figures (2).

3. Multiplication by 100:
   \[
   0.003208 \times 100 = 0.3208
   \]
   This value will be rounded to **2 significant figures**, as dictated by earlier steps.

So, the final result is **0.32%**.

Would you like further clarification or details on this?

Here are 5 related questions for further exploration:
1. How do significant figures affect the precision of a calculation?
2. Why does the number of decimal places matter in subtraction?
3. What is the rule for rounding when performing division with different significant figures?
4. How do significant figures influence percentage error calculations?
5. How does scientific notation affect significant figures in large numbers?

**Tip:** Always apply the rule of least significant figures when combining numbers with different precision to avoid overestimating the accuracy of your result.

((2.0265 - 2.02)/2.0265) * 100.00 with significant figures

Learn how to calculate the percentage difference between 2.0265 and 2.02 while applying significant figure rules. This detailed solution covers subtraction, division, and percentage multiplication, ensuring proper handling of significant figures. Suitable for students in Grades 9-12.

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