Calculating Percentage Error: What to Do and How to Do It

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Percentage error is calculated by taking the difference between a measured value and an accepted value, dividing that difference by the accepted value, and then multiplying by 100%. For example, if the measured atomic molar mass of lithium is 8 g/mol and the accepted value is 6.94 g/mol, the difference is 1.06 g/mol, resulting in a percent error of +15.27%. In situations where the true value is unknown, the estimated error can be divided by the measured value instead. Understanding these calculations is essential for accurately assessing measurement accuracy. This method provides a framework for evaluating errors in scientific measurements.
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I forgot how to do percentage error, actually I kind of forgot what it is. I do remember multiplying somthg by 100% but i can't remember what i divide b4 that.
 
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In terms of percent error with regards to an accepted value:
Suppose you measured the atomic molar mass of lithium to be 8 g/mol. The accepted value is 6.94. You take the difference, which is 1.06g/mol, and the percent error is therefore +15.27% ie. 1.06/6.94 * 100%
 
Theoretically, you divide the error by the true value. In practice, you have an error because you don't know the true value! In that case you divide the (estimated error) by the measured value.
 
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
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