Question

A piece of wood has a labeled length value of 63.2 cm. You measure its length three times and record the following data: 63.1 cm, 63.0 cm, and 63.7 cm. Calculate the percent error for each measurement.

Answer 1

Percent error (%)=
`(\left | Accepted value - Measured value \right |)/(Accepted value)* 100`

Accepted value is true value.

Measured values is calculated value.

In the question given Accepted value (true value) = 63.2 cm

Given Measured(calculated values) = 63.1 cm , 63.0 cm , 63.7 cm

1) Percent error (%) for first measurement.

Accepted value (true value) = 63.2 cm, Measured(calculated values) = 63.1 cm

Percent error (%)=
`(\left | Accepted value - Measured value \right |)/(Accepted value)* 100`

`Percent error = (\left | 63.2 - 63.1 \right |)/(63.2)* 100`

`Percent error = (0.1)/(63.2)* 100`

`Percent error = 0.00158* 100`

Percent error = 0.158 %

2) Percent error (%) for second measurement.

Accepted value (true value) = 63.2 cm, Measured(calculated values) = 63.0 cm

Percent error (%)=
`(\left | Accepted value - Measured value \right |)/(Accepted value)* 100`

`Percent error = (\left | 63.2 - 63.0 \right |)/(63.2)* 100`

`Percent error = (0.2)/(63.2)* 100`

`Percent error = 0.00316* 100`

Percent error = 0.316 %

3) Percent error (%) for third measurement.

Accepted value (true value) = 63.2 cm, Measured(calculated values) = 63.7 cm

Percent error (%)=
`(\left | Accepted value - Measured value \right |)/(Accepted value)* 100`

`Percent error = (\left | 63.2 - 63.7 \right |)/(63.2)* 100`

`Percent error = (\left | -0.5 \right |)/(63.2)* 100`

`Percent error = ((0.5))/(63.2)* 100`

`Percent error = 0.00791* 100`

Percent error = 0.791 %

Percent error for each measurement is :

63.1 cm = 0.158%

63.0 cm = 0.316%

63.7 cm = 0.791%