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)
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