Solved on Dec 15, 2023

Find the percent error of a measurement of a 18-inch line that was measured as 17.3 inches, rounded to the nearest tenth of a percent.

STEP 1

Assumptions
1. The measured length of the line is 17.3 inches.
2. The actual length of the line is 18 inches.
3. Percent error is calculated using the formula:
$\text{Percent error} = \left( \frac{\text{Absolute value of the error}}{\text{Actual value}} \right) \times 100\%$

STEP 2

Calculate the absolute value of the error by subtracting the measured value from the actual value.
$\text{Error} = \text{Actual value} - \text{Measured value}$

STEP 3

Now, plug in the given values for the actual and measured lengths to calculate the error.
$\text{Error} = 18\, \text{inches} - 17.3\, \text{inches}$

STEP 4

Calculate the error.
$\text{Error} = 18 - 17.3 = 0.7\, \text{inches}$

STEP 5

Now that we have the error, we can calculate the percent error using the formula provided in STEP_1.
$\text{Percent error} = \left( \frac{\text{Error}}{\text{Actual value}} \right) \times 100\%$

STEP 6

Plug in the values for the error and the actual length to calculate the percent error.
$\text{Percent error} = \left( \frac{0.7}{18} \right) \times 100\%$

STEP 7

Calculate the percent error.
$\text{Percent error} = \left( \frac{0.7}{18} \right) \times 100\% \approx 3.888\%$

STEP 8

Round the percent error to the nearest tenth of a percent.
$\text{Percent error} \approx 3.9\%$
The percent error of the measurement is approximately 3.9%.

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Find the percent error of a measurement of a 18-inch line that was measured as 17.3 inches, rounded to the nearest tenth of a percent.

STEP 1

Assumptions
1. The measured length of the line is 17.3 inches.
2. The actual length of the line is 18 inches.
3. Percent error is calculated using the formula:
$\text{Percent error} = \left( \frac{\text{Absolute value of the error}}{\text{Actual value}} \right) \times 100\%$

STEP 2

Calculate the absolute value of the error by subtracting the measured value from the actual value.
$\text{Error} = \text{Actual value} - \text{Measured value}$

STEP 3

Now, plug in the given values for the actual and measured lengths to calculate the error.
$\text{Error} = 18\, \text{inches} - 17.3\, \text{inches}$

STEP 4

Calculate the error.
$\text{Error} = 18 - 17.3 = 0.7\, \text{inches}$

STEP 5

Now that we have the error, we can calculate the percent error using the formula provided in STEP_1.
$\text{Percent error} = \left( \frac{\text{Error}}{\text{Actual value}} \right) \times 100\%$

STEP 6

Plug in the values for the error and the actual length to calculate the percent error.
$\text{Percent error} = \left( \frac{0.7}{18} \right) \times 100\%$

STEP 7

Calculate the percent error.
$\text{Percent error} = \left( \frac{0.7}{18} \right) \times 100\% \approx 3.888\%$

STEP 8

Round the percent error to the nearest tenth of a percent.
$\text{Percent error} \approx 3.9\%$
The percent error of the measurement is approximately 3.9%.

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Find the percent error of a measurement of a 18-inch line that was measured as 17.3 inches, rounded to the nearest tenth of a percent.

STEP 1

STEP 2

Calculate the absolute value of the error by subtracting the measured value from the actual value.Error=Actual value−Measured value\text{Error} = \text{Actual value} - \text{Measured value}Error=Actual value−Measured value

STEP 3

Now, plug in the given values for the actual and measured lengths to calculate the error.Error=18 inches−17.3 inches\text{Error} = 18\, \text{inches} - 17.3\, \text{inches}Error=18inches−17.3inches

STEP 4

Calculate the error.Error=18−17.3=0.7 inches\text{Error} = 18 - 17.3 = 0.7\, \text{inches}Error=18−17.3=0.7inches

STEP 5

Now that we have the error, we can calculate the percent error using the formula provided in STEP_1.Percent error=(ErrorActual value)×100%\text{Percent error} = \left( \frac{\text{Error}}{\text{Actual value}} \right) \times 100\%Percent error=(Actual valueError​)×100%

STEP 6

Plug in the values for the error and the actual length to calculate the percent error.Percent error=(0.718)×100%\text{Percent error} = \left( \frac{0.7}{18} \right) \times 100\%Percent error=(180.7​)×100%

STEP 7

Calculate the percent error.Percent error=(0.718)×100%≈3.888%\text{Percent error} = \left( \frac{0.7}{18} \right) \times 100\% \approx 3.888\%Percent error=(180.7​)×100%≈3.888%

STEP 8

Round the percent error to the nearest tenth of a percent.Percent error≈3.9%\text{Percent error} \approx 3.9\%Percent error≈3.9%The percent error of the measurement is approximately 3.9%.

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Calculate the absolute value of the error by subtracting the measured value from the actual value.
$\text{Error} = \text{Actual value} - \text{Measured value}$

Now, plug in the given values for the actual and measured lengths to calculate the error.
$\text{Error} = 18\, \text{inches} - 17.3\, \text{inches}$

Calculate the error.
$\text{Error} = 18 - 17.3 = 0.7\, \text{inches}$

Now that we have the error, we can calculate the percent error using the formula provided in STEP_1.
$\text{Percent error} = \left( \frac{\text{Error}}{\text{Actual value}} \right) \times 100\%$

Plug in the values for the error and the actual length to calculate the percent error.
$\text{Percent error} = \left( \frac{0.7}{18} \right) \times 100\%$

Calculate the percent error.
$\text{Percent error} = \left( \frac{0.7}{18} \right) \times 100\% \approx 3.888\%$

Round the percent error to the nearest tenth of a percent.
$\text{Percent error} \approx 3.9\%$
The percent error of the measurement is approximately 3.9%.