Question

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?

Answer 1

`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"`