# Numerical Ranges

Consider this sample question:

* Sample question: What is the area of a circle of radius 5cm? Give your answer in cm^2.*

If a student uses 3.14 as their value for PI, then they would get an answer of 3.14 * 5^{2} = 78.500 cm^{2}. But if they use 3.14159, they would get: 3.14159 * 5^2 = 78.5398 cm^{2}. As an instructor, you probably want to mark both possible answers as correct (and anything in-between).

To ensure Flubaroo does this, you can enter your answer key in two ways:

78.5 **%to** 78.54

or

78.5 **%pm** 1.5%

The special **%to** operator tells Flubaroo to expect a numerical answer that falls between the numbers given. Strictly, for a range of **A %to B**, an answer x will be correct if A **<=** x **<=** B (note the equals signs).

The special **%pm** operator will allow a **plus-minus** percentage range. So for **A %pm 1.5%, **an answer x will be correct if in the range A * (0.985) <= x <= A * (1.015).

But wait, there's more....

Because Flubaroo is expecting a numerical input for this question, the student could also enter 7.85e1 (shorthand for 7.85 * 10^{1}), and Flubaroo will also mark is as correct. So you see, a student can enter their answer in a variety of numerical formats, and all will be graded as correct so long as they fall within the acceptable number range. So all of the following submissions would marked as correct: 78.5, 7.58e1, 785e-1, etc....

Lastly, we all know that students make mistakes when entering answers. Specifically, a student may not realize that you're looking for just the numerical part of the answer, and might also include the units like this: 78.53cm2. Don't worry, before grading Flubaroo will throw away any text following the number, so this will be marked as correct too!