Question

What is the percentage error of 19.75 over 30

Answer 1

To calculate the percentage error of a value, you can use the formula:

\[
\text{Percentage Error} = \left(\frac{\text{Actual Value} - \text{Expected Value}}{\text{Expected Value}}\right) \times 100
\]

In this context, if we consider "19.75" as the actual value and "30" as the expected value, the formula becomes:

\[
\text{Percentage Error} = \left(\frac{19.75 - 30}{30}\right) \times 100
\]

Calculating this step-by-step:

1. Subtract the expected value from the actual value:
\( 19.75 - 30 = -10.25 \)

2. Divide by the expected value:
\(-10.25 / 30 \approx -0.34167\)

3. Multiply by 100 to get the percentage:
\(-0.34167 \times 100 \approx -34.17\%\)

The percentage error is approximately \(-34.17\%\).

The negative sign indicates that the actual value is less than the expected value. If you're only interested in the magnitude of the error, you can say the percentage error is \(34.17\%\).