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

Question

[(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: $$\text{Extra open brace or missing close brace}$$

Summary of Significant Figures

• Calculator answer before multiplication: $0.003207$ (four significant digits)
• Percentage result: $0.3207$ (four significant digits)