# Question 14f6c

Aug 17, 2017

The smaller the percent error, the more accurate the results are.

#### Explanation:

Example:

"Percent error"=abs(("accepted value"-"experimental value")/("accepted value"))xx100

Example:

Maria determined that a cylinder of aluminum had a density of ${\text{2.74 g/cm}}^{3}$. The actual value is ${\text{2.70 g/cm}}^{3}$. What is her percent error?

"Percent error"=abs(("2.70 g/cm"^3-"2.74 g/cm"^3)/("2.70 g/cm"^3))xx100

"Percent error"=1.48%

Henry determined that the same cylinder of aluminum had a density of ${\text{2.69 g/cm}}^{3}$. What is his percent error?

"Percent error"=abs(("2.70 g/cm"^3-"2.69 g/cm"^3)/("2.70 g/cm"^3"))xx100=0.388%

As you can see, Henry had the more accurate result because his percent error was less than Maria's.

Aug 17, 2017

percent error and accuracy are inversely proportional to each other

#### Explanation:

The short answer is the "math" way of putting it. As percent error increases, accuracy decreases. Let's look at the equation. I will present it in two different formats. Just use the one your teacher prefers. The only difference between the two is whether or not your teacher prefers % error to be positive only.

The first variable is ${x}_{m e a s u red}$ — the result you experimentally obtained.
The second variable is ${x}_{t r u e}$ — the accepted or theoretical result you should get.

% error = (x_(measured) - x_(true))/x_(true)*100%

OR

% error =abs((x_(measured) - x_(true))/x_(true))*100%#

Inaccuracy is due to random (indeterminate) or systematic (determinate) error.

Random (indeterminate) error results from uncontrollable variables when taking a measurement. This type of error is always present and (usually) never correctable. An example of this would be electric noises or environmental factors. Two ways to reduce random error is to take more measurements or do some statistical analysis. A larger sample can reduce the fluctuations

Systematic (determinate) error results from instruments and/or procedures. This error is reproducible and can be hard to detect. This is where you get "user error". Another example of this would be incorrectly taring a balance or not calibrating your equipment/instruments.