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

Question

[(11.34 - 9.63) / 11.34] x 100.00

make it more clear.

Answer 1

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.