Math Snap

STEP 1

Assumptions1. The measured value is $90.7 \mathrm{~kg}$
. The true value is $60.0 \mathrm{~kg}$
3. Absolute error is calculated as the absolute difference between the true value and the measured value4. Relative error is calculated as the absolute error divided by the true value

STEP 2

First, we need to calculate the absolute error. The absolute error is the absolute difference between the true value and the measured value.
$$Absolute\, error = |Measured\, value - True\, value|$$

STEP 3

Now, plug in the given values for the measured value and the true value to calculate the absolute error.
$$Absolute\, error = |90.7 \mathrm{~kg} -60.0 \mathrm{~kg}|$$

STEP 4

Calculate the absolute error.
$$Absolute\, error = |90.7 \mathrm{~kg} -60.0 \mathrm{~kg}| =30.7 \mathrm{~kg}$$

STEP 5

Next, we need to calculate the relative error. The relative error is the absolute error divided by the true value.
$$Relative\, error = \frac{Absolute\, error}{True\, value}$$

STEP 6

Now, plug in the values for the absolute error and the true value to calculate the relative error.
$$Relative\, error = \frac{30. \mathrm{~kg}}{60.0 \mathrm{~kg}}$$

STEP 7

Calculate the relative error.
$$Relative\, error = \frac{30.7 \mathrm{~kg}}{60.0 \mathrm{~kg}} =0.511666...$$

STEP 8

The relative error is a ratio and does not have units. Also, it is often expressed as a percentage. So, we multiply the decimal by100 to get a percentage.
$$Relative\, error =0.511666... \times100\%$$

Calculate the relative error as a percentage.
$$Relative\, error =.511666... \times100\% =51.17\%$$The absolute error of the scientist's measurement is $30.7 \mathrm{~kg}$ and the relative error is $51.17\%$.