A handbook gives the density of calcium as "1.62 g/cm"^3. What is the percent error of a density calculation of "1.37 g/cm"^3 based on lab measurements?

1 Answer
Stefan V.
Sep 20, 2017

15.4%

Explanation:

Your tool of choice here will be the following equation

"% error" = (|"accepted value " - " measured value"|)/"accepted value" * 100%

So what you're looking for here is the absolute value of the difference between the accepted value and the measured value expressed as a percentage of the accepted value.

In your case, you have

  • "accepted value" = "1.62 g cm"^(-3)
  • "measured value" = "1.37 g cm"^(-3)

Plug this in the equation to get

"% error" = (|(1.62 - 1.37)color(red)(cancel(color(black)("g cm"^(-3))))|)/(1.62color(red)(cancel(color(black)("g cm"^(-3))))) * 100%

color(darkgreen)(ul(color(black)("% error" = 15.4%)))

The answer is rounded to three sig figs.

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