Question

show the calculator answer, significant digits answer and identify the number of significant digits. show all work.
[(2.0265 - 2.02) / 2.0265] x 100.00

make it more clear.

Answer 1

To solve the expression \(\left[\frac{(2.0265 - 2.02)}{2.0265}\right] \times 100.00\) and check the appropriate significant digits, we follow these steps clearly:

### Step 1: Perform the subtraction
We first find the difference:
\[
2.0265 - 2.02 = 0.0065
\]

### Step 2: Divide by 2.0265
Now we divide the result from Step 1 by 2.0265:
\[
\frac{0.0065}{2.0265} \approx 0.003207
\]

### Step 3: Convert to percentage
Next, we multiply the result by 100.00 to convert to a percentage:
\[
0.003207 \times 100.00 = 0.3207
\]

### Step 4: Determine significant digits
- In the subtraction \(2.0265 - 2.02\), the value of \(2.02\) has **three significant digits** (it’s defined to the hundredths place), affecting the result of the subtraction: **0.0065** (which has four significant digits).
- When we divide \(0.0065\) by \(2.0265\), the result \(\approx 0.003207\) should retain significant figures based on the limiting term. Here \(2.0265\) has **five significant digits** and \(0.0065\) has four. Thus, the result should keep four digits.
- Now, we convert \(0.003207\) to a percentage, resulting in **0.3207%**.

### Final Result
The final result is:
\[
\boxed{0.3207\%}
\]

### Summary of Significant Figures
- Calculator answer before multiplication: \(0.003207\) (four significant digits)
- Percentage result: \(0.3207\%\) (four significant digits)