# A student obtains a percent error of 20% after finding that the true value for the mass of an object is 50 grams. What is the student's value?

Nov 13, 2015

${m}_{\text{exp" = "40 g" " }}$ or $\text{ "m_"exp" = "60 g}$

#### Explanation:

Percent error is defined as the difference between the experimental value and the theoretical value, taken in absolute value, divided by the theoretical value, and multiplied by $100$

color(blue)("% error" = (|"experimental value" - "theoretical value"|)/(|"theoretical value"|))

In your case, the percent error is equal to 20% and the theoretical value, or true value, for the mass of the object is given as $\text{50 g}$.

If $x$ is the experimental mass of the object, then you can say that

20% = (|x - 50|)/50 xx 100

This is equivalent to

$| x - 50 | = \frac{20 \cdot 50}{100}$

$| x - 50 | = 10$

Now, this equation has two solutions, one for $| x - 50 | \ge 0$, for which

$| x - 50 | = x - 50$

and you have

$x - 50 = 10 \implies x = 60$

and for when $| x - 5 | < 0$, which given you

$| x - 50 | = - \left(x - 50\right) = - x + 50$

$- x + 50 = 10 \implies x = 40$

Therefore, the experimental mass of the object can be

${m}_{\text{exp" = "40 g" " }}$ or $\text{ "m_"exp" = "60 g}$