Solved on Aug 17, 2023

Find the max error of a $2.5 \pm 0.5 \mathrm{~kg}$ newborn weight measurement. Calculate the percentage error.

STEP 1

Assumptions1. The weight of the new-born baby is measured to be $.5 \mathrm{~kg}$ , correct to the nearest $0.5 \mathrm{~kg}$ . . The maximum absolute error is half the unit of measurement.
3. The percentage error is calculated by dividing the absolute error by the measured value and multiplying by100.

STEP 2

First, we need to find the maximum absolute error of the measurement. This is half the unit of measurement.
$Absolute\, error = \frac{Unit\, of\, measurement}{2}$

STEP 3

Now, plug in the given value for the unit of measurement to calculate the absolute error.
$Absolute\, error = \frac{0.5 \mathrm{~kg}}{2}$

STEP 4

Calculate the absolute error.
$Absolute\, error = \frac{0. \mathrm{~kg}}{2} =0.25 \mathrm{~kg}$

STEP 5

Now that we have the absolute error, we can find the percentage error. This is calculated by dividing the absolute error by the measured value and multiplying by100.
$Percentage\, error = \left(\frac{Absolute\, error}{Measured\, value}\right) \times100\%$

STEP 6

Plug in the values for the absolute error and the measured value to calculate the percentage error.
$Percentage\, error = \left(\frac{0.25 \mathrm{~kg}}{2.5 \mathrm{~kg}}\right) \times100\%$

STEP 7

Calculate the percentage error.
$Percentage\, error = \left(\frac{0.25 \mathrm{~kg}}{2.5 \mathrm{~kg}}\right) \times100\% =10\%$ (a) The maximum absolute error of the measurement is $0.25 \mathrm{~kg}$ .
(b) The percentage error of the measurement is $10\%$ .

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Find the max error of a $2.5 \pm 0.5 \mathrm{~kg}$ newborn weight measurement. Calculate the percentage error.

STEP 1

STEP 2

First, we need to find the maximum absolute error of the measurement. This is half the unit of measurement.
$Absolute\, error = \frac{Unit\, of\, measurement}{2}$

STEP 3

Now, plug in the given value for the unit of measurement to calculate the absolute error.
$Absolute\, error = \frac{0.5 \mathrm{~kg}}{2}$

STEP 4

Calculate the absolute error.
$Absolute\, error = \frac{0. \mathrm{~kg}}{2} =0.25 \mathrm{~kg}$

STEP 5

Now that we have the absolute error, we can find the percentage error. This is calculated by dividing the absolute error by the measured value and multiplying by100.
$Percentage\, error = \left(\frac{Absolute\, error}{Measured\, value}\right) \times100\%$

STEP 6

Plug in the values for the absolute error and the measured value to calculate the percentage error.
$Percentage\, error = \left(\frac{0.25 \mathrm{~kg}}{2.5 \mathrm{~kg}}\right) \times100\%$

STEP 7

Calculate the percentage error.
$Percentage\, error = \left(\frac{0.25 \mathrm{~kg}}{2.5 \mathrm{~kg}}\right) \times100\% =10\%$ (a) The maximum absolute error of the measurement is $0.25 \mathrm{~kg}$ .
(b) The percentage error of the measurement is $10\%$ .

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Find the max error of a 2.5±0.5 kg2.5 \pm 0.5 \mathrm{~kg}2.5±0.5 kg newborn weight measurement. Calculate the percentage error.

STEP 1

STEP 2

First, we need to find the maximum absolute error of the measurement. This is half the unit of measurement.Absolute error=Unit of measurement2Absolute\, error = \frac{Unit\, of\, measurement}{2}Absoluteerror=2Unitofmeasurement​

STEP 3

Now, plug in the given value for the unit of measurement to calculate the absolute error.Absolute error=0.5 kg2Absolute\, error = \frac{0.5 \mathrm{~kg}}{2}Absoluteerror=20.5 kg​

STEP 4

Calculate the absolute error.Absolute error=0. kg2=0.25 kgAbsolute\, error = \frac{0. \mathrm{~kg}}{2} =0.25 \mathrm{~kg}Absoluteerror=20. kg​=0.25 kg

STEP 5

STEP 6

Plug in the values for the absolute error and the measured value to calculate the percentage error.Percentage error=(0.25 kg2.5 kg)×100%Percentage\, error = \left(\frac{0.25 \mathrm{~kg}}{2.5 \mathrm{~kg}}\right) \times100\%Percentageerror=(2.5 kg0.25 kg​)×100%

STEP 7

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Find the max error of a $2.5 \pm 0.5 \mathrm{~kg}$ newborn weight measurement. Calculate the percentage error.

First, we need to find the maximum absolute error of the measurement. This is half the unit of measurement.
$Absolute\, error = \frac{Unit\, of\, measurement}{2}$

Now, plug in the given value for the unit of measurement to calculate the absolute error.
$Absolute\, error = \frac{0.5 \mathrm{~kg}}{2}$

Calculate the absolute error.
$Absolute\, error = \frac{0. \mathrm{~kg}}{2} =0.25 \mathrm{~kg}$

Plug in the values for the absolute error and the measured value to calculate the percentage error.
$Percentage\, error = \left(\frac{0.25 \mathrm{~kg}}{2.5 \mathrm{~kg}}\right) \times100\%$