Studdy AI Logo
Math

QuestionA scientist measures 90.7 kg90.7 \mathrm{~kg}, while the true value is 60.0 kg60.0 \mathrm{~kg}. Find the absolute and relative error.

Studdy Solution

STEP 1

Assumptions1. The measured value is 90.7 kg90.7 \mathrm{~kg} . The true value is 60.0 kg60.0 \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∣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 kg−60.0 kg∣Absolute\, error = |90.7 \mathrm{~kg} -60.0 \mathrm{~kg}|

STEP 4

Calculate the absolute error.
Absolute error=∣90.7 kg−60.0 kg∣=30.7 kgAbsolute\, 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=Absolute errorTrue valueRelative\, 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=30. kg60.0 kgRelative\, error = \frac{30. \mathrm{~kg}}{60.0 \mathrm{~kg}}

STEP 7

Calculate the relative error.
Relative error=30.7 kg60.0 kg=0.511666...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...×100%Relative\, error =0.511666... \times100\%

STEP 9

Calculate the relative error as a percentage.
Relative error=.511666...×100%=51.17%Relative\, error =.511666... \times100\% =51.17\%The absolute error of the scientist's measurement is 30.7 kg30.7 \mathrm{~kg} and the relative error is 51.17%51.17\%.

Was this helpful?

Studdy solves anything!

banner

Start learning now

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

ParentsInfluencer programContactPolicyTerms
TwitterInstagramFacebookTikTokDiscord