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
Nov 13, 2015

Answer:

#m_"exp" = "40 g" " "# or #" "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 #"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| = (20 * 50)/100#

#|x-50| = 10#

Now, this equation has two solutions, one for #|x-50|>=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| = -(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"#