Let's break down the calculation step by step, highlighting the significant digits for each step and showing the final results clearly.
Step 1: Perform the subtraction
\[ 11.34 - 9.63 \]
Calculation: \[ 11.34 - 9.63 = 1.71 \]
Significant Digits:
- The number 11.34 has 4 significant digits.
- The number 9.63 has 3 significant digits.
- The result, 1.71, is reported to 3 significant digits because the least precise measurement (9.63) has 3 significant digits.
Step 2: Divide by 11.34
\[ \frac{1.71}{11.34} \]
Calculation: \[ \frac{1.71}{11.34} \approx 0.1507 \]
Significant Digits:
- The number 1.71 has 3 significant digits.
- The number 11.34 has 4 significant digits.
- Therefore, the result should be reported with 3 significant digits, which means we will keep 0.1507 and round it to 0.151.
Step 3: Multiply by 100.00
\[ 0.151 \times 100.00 \]
Calculation: \[ 0.151 \times 100.00 = 15.1 \]
Significant Digits:
- The number 0.151 has 3 significant digits.
- The number 100.00 has 5 significant digits.
- The final result must be reported with 3 significant digits because of the calculation with 0.151.
Final Answer
Thus, the final answer is: \[ \text{Percentage Change} = 15.1 % \]
Summary
- Calculator Answer: 15.1
- Significant Digits Answer: 15.1
- Number of Significant Digits: 3
This concludes the calculation, and the answer is clearly stated with significant digits considered at each step.