Question

A student calculates the density of iron as 6.6 g/cm3 using lab data for mass and volume. A handbook reveals that the correct value is 7.57 g/cm3. What is the percent error?

Answer 1

`% "error" = 12.8%`

Explanation:

Percent error is calculated using the following formula:

`Rightarrow % "error" = |frac("experimental value" - "theoretical value")("theoretical value")| cdot 100`

This formula can be refined as:

`Rightarrow % "error" = |frac("experimental value")("theoretical value") - frac("theoretical value")("theoretical value")| cdot 100`

`Rightarrow % "error" = |frac("experimental value")("theoretical value") - 1| cdot 100`

Now, let's substitute the relevant values into the formula:

`Rightarrow % "error" = |frac(6.6" g/cm"^(3))(7.57" g/cm"^(3)) - 1| cdot 100`

`Rightarrow % "error" = |0.8718626156 - 1| cdot 100`

`Rightarrow % "error" = |- 0.1281373844| cdot 100`

`Rightarrow % "error" = 0.1281373844 cdot 100`

`Rightarrow % "error" = 12.81373844%`

`therefore % "error" approx 12.8%`

Therefore, the percent error is around `12.8%`.