Question

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