Questions: =0.01 sqrt(((0.0001/0.9317)^2+((0.00012/0.250)^2))

Solution Steps

To solve the given mathematical expression, we need to follow these steps:

1. Calculate the square of the fraction \(\frac{0.0001}{0.9317}\).
2. Calculate the square of the fraction \(\frac{0.00012}{0.250}\).
3. Add the results from steps 1 and 2.
4. Take the square root of the sum obtained in step 3.
5. Multiply the result by 0.01 to get the final answer.

We start by calculating the square of the fraction: \[ \left(\frac{0.0001}{0.9317}\right)^{2} \approx 1.4301 \times 10^{-8} \]

Next, we calculate the square of the second fraction: \[ \left(\frac{0.00012}{0.250}\right)^{2} \approx 2.304 \times 10^{-8} \]

Now, we add the results from Step 1 and Step 2: \[ 1.4301 \times 10^{-8} + 2.304 \times 10^{-8} \approx 3.7341 \times 10^{-8} \]

We take the square root of the sum obtained in Step 3: \[ \sqrt{3.7341 \times 10^{-8}} \approx 6.103 \times 10^{-4} \]

Finally, we multiply the result by \(0.01\): \[ 0.01 \times 6.103 \times 10^{-4} \approx 4.9185 \times 10^{-6} \]

Final Answer