# Accuracy settings

For the algebra interaction, AlgebraKiT currently supports four different accuracy settings. To add this setting, click Actions > Accuracy.

You will then be able to select one of the following settings.

Exact

The default behaviour of AlgebraKiT is the exact accuracy setting. That means that no answer other than the mathematically exact answer to the question is accepted. The knowledge set of the selected audience defines what is mathematically exact for the student.

Rounded to

With the rounded to setting, the student has to write the answer rounded to exactly the selected number of decimals.

In the worked solution, AlgebraKiT will show the answer rounded to the selected number of decimals.

Accurate to

With the accurate to setting selected, the student has to write the answer rounded to at least the selected number of decimals correctly.

In the worked solution, AlgebraKiT will show the answer rounded to the least number of decimals.

Range

With the range setting selected, the answer of the student should lie between the boundaries entered ($minimum \le student input \le maximum$).

In the worked solution, AlgebraKiT will show the $maximum$ boundary value as solution.

Note that there is also some change in behavior related to the accuracy setting. This is explained below.

Accuracy settings – accepted input behavior

Answer rounded to 1 d.p. means that any input of the student is correct (not finished) if that input rounded to 1 d.p. will result in the original required value rounded to 1 d.p.

Why? A student might need to do more advanced calculations to calculate the final value. If a student chooses to round the intermediate steps to a different amount of decimals than you authored (but still enough to get to the correct final answer), it might be that the intermediate calculations differ from the exact value of the original result before rounding.

##### Example

$x=\frac{1}{7}$
$x^3=0.00291545189$ rounded to 11 d.p.
$x^3=0.003$ rounded to 3 d.p.

When calculating $x^3$ using $x$ rounded to $6$ decimals gives $(0.142857)^3=0.00291544314$. The margin of error seems quite small, but it is still there. However, rounded to 3 d.p. it yields the same result as using the exact value of $x$ for the calculation.

When calculating $x^3$ using $x$ rounded to $3$ decimals gives $(0.143)^3=0.002924207$. The margin of error gets bigger, but still, rounded to 3 d.p. it yields the same result as using the exact value of $x$ for the calculation.

As we can’t limit the student by always using exact values in their calculation, the above behavior applies to questions with accuracy settings applied.

In the below interactive exercise you can try all of the above (the exercise definition can be found here in the AlgebraKiT library):