# 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?

##### 1 Answer

#### 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

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

In your case, the percent error is equal to

If

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

This is equivalent to

#|x-50| = (20 * 50)/100#

#|x-50| = 10#

Now, this equation has two solutions, one for

#|x-50| = x-50#

and you have

#x - 50 = 10 implies x = 60#

and for when

#|x - 50| = -(x-50) = -x + 50#

#-x + 50 = 10 implies x = 40#

Therefore, the experimental mass of the object can be

#m_"exp" = "40 g" " "# or#" "m_"exp" = "60 g"#