David measures a line to be 5.25 in long. If the actual measurement is 5 in, find David's relative error to the nearest thousandth.

Answer 1

To find David's relative error, we first need to calculate the absolute error and then use it to find the relative error.

1. Calculate the absolute error: $$\text{Absolute Error}=|\text{Measured Value}-\text{Actual Value}|$$ Given that David measured 5.25 inches and the actual measurement is 5 inches, we have: $$\text{Absolute Error}=|5.25-5|=|0.25|=0.25\text{ inches}$$

2. Calculate the relative error: $$\text{Relative Error}=\frac{\text{Absolute Error}}{\text{Actual Value}}$$ Using the absolute error we calculated and the actual value (5 inches): $$\text{Relative Error}=\frac{0.25}{5}$$

   Performing the division: $$\text{Relative Error}=0.05$$

3. Convert the relative error to a percentage (if needed): To express the relative error as a percentage, we multiply by 100: $$\text{Relative Error (percentage)}=0.05\times 100=5$$

4. Final Representation as a Decimal: Since you asked for the relative error to the nearest thousandth as a decimal, we write: $$\text{Relative Error}=0.050$$

Thus, David's relative error, to the nearest thousandth, is 0.050.