Numeric values with units of measurement

About answer equivalence for numeric with units answers

When evaluating the equivalence of a student submission to the correct and incorrect answers you code, the Mastering answer engine uses the following guidelines:

The units students enter are compared to the units for the correct answer before the numeric values. If the units are not equivalent, no comparison of the numeric values are made.

The equivalence of the numeric portion of any two physical quantities follows the same rules as for answers in the numeric value expression answer type.
That is, incorrect items that evaluate as equal (within tolerance) to a specific pre-defined value according to the algorithm used in the answer engine, are considered equivalent.
However, there is one exception: Students cannot enter mathematical expressions into the numeric value with units answer type. For example, students can't enter 12+12 in this answer type, even though that entry is acceptable for numeric value or expression answers.

Combinations of base units: In most cases, students can enter combinations of base units even when there is a standard unit monomial. For example, a student can enter “kg*m/s^2” in place of “N” for SI units of force.
Supported SI prefixes: SI prefixes are recognized only on those units explicitly identified in the list of supported prefixes and units.
Supported compound units: Compound units are supported only as identified in the list of supported prefixes and units, regardless of whether the constituent base units are supported.
Zero numeric value: When both your answer and the student entry have a numeric value that is zero, they are equivalent even if one has a unit and the other does not.
Two physical quantities expressed in different unit systems: These are NEVER equivalent.
Two unit monomials: These are equivalent only if they are identical, including case (J and j are not the same).
Two physical quantities expressed in different units: These are equivalent if their numerical value is equal (within tolerance) after converting both to the same unit. For example, “1 ft” and “12 in” are equivalent. Compound units are converted as a whole; base units are not individually converted.
Temperature units: These are NOT equivalent. If an answer is either degrees Celsius or kelvin, you should code an alternate correct answer in kelvin or degrees Celsius. The conversion between temperature scales is prohibited because a temperature reading of 10 K converts to Celsius differently than a temperature change of 10 K.

To determine whether two compound units are equivalent:

They must involve identical base units. The following are not equivalent:
They must be mathematically equivalent, treating each base unit as a variable. The following are all equivalent:
Base units can be in any order. The following are equivalent:
Base units must be to the same power. The following are not equivalent.
They are acknowledged to measure the same physical quantity and reduce to the same combination of base units. For example, electric potential (V), can be reported in units of J/C and W/A. The list of supported prefixes and units contains compound units considered equivalent for various physical quantities.
Multiplication must be explicit, either via multiplication symbols or templates. The following are not equivalent:
Both cdot and dash are acceptable multiplication symbols for compound units. You must use * for multiplication in compound units when you code correct and incorrect answers. The following are equivalent:

Specify exact unit match for the correct answer

When you want students to explicitly match the unit answer you provide, check the box for "Exact unit match".

Add solve for, pre-text, or post-text (Optional)

Select the add solve for link to enter text or a mathematical expression that will appear before "=", such as "m , x". The equals sign is supplied for the answer—you don't have to enter it.
Select the add pre-text link to enter text to appear before the answer.
Select the add post-text link to enter text to appear after the answer.

Set tolerance and rounding message (Optional)

For numeric answers, student answers are considered correct if they match the coded answer to the specified grading tolerance. In general, you can accept the default tolerance value of 2%.

To change the grading tolerance
Specify another value in the box for Acceptable variation or rounding error. For more information on grading tolerance, see Significant figures and tolerance.
To show the rounding message to students
Select the check box for Show additional rounding message... when the student response from the current part is used for a calculation of a subsequent part. For example, the student calculates a response for Part A. The response from part A is needed in the calculation of Part B. The student should use the full precision number from Part A in the Part B calculation.
The additional rounding messages that displays to students is:
"If you need this result for any later calculation in this item, keep all the digits and round as the final step before submitting your answer."
For more details, see How significant figures and tolerance work in Mastering and/or Guidelines for setting significant figures and tolerance.

Add the correct answer and optionally adjust significant figures display

Under Correct Answer, enter the correct answers in the Number (that is, a numeric value) and Units boxes.
- Numeric value answer Enter a numeric value or expression. See also the section above, "About numeric equivalence for numeric with units answers".
  Mastering Physics and Mastering Engineering vector notation
  You must code vector answer values using infix, with subscripts using tags that end in either vec or evec. For physics: F_k_vec is the only acceptable notation for vectors with subscript answer values. For engineering: F_k_evec is the only acceptable notation for vectors with subscript answer values.
- Units answer
  Enter an accepted unit. Use * for multiplication in compound units.
  For instructions on entering units, see Accepted units that Mastering recognizes. Select the Preview link to view the rendered units expression in a different box.
Set the answer format (display of significant figures).
Numeric answers are displayed to 3 significant figures, without using scientific notation for values like 200. Mastering evaluates the student answer against the truncated formatted correct answer.
When this box is blank, the default value of 3 significant figures is in effect; only enter a value if you want to change the default value. More information about significant figures
Add an alternate correct answer.
Select the add an additional correct answer link and add another set of Number and Units answers.
About degrees Celsius and degrees kelvin units: The units of degrees Celsius and kelvin are NOT considered equivalent units when matching students’ answers. If you want both units to be accepted, add correct answers for both units. For an exact match, you just need to provide one answer, since the system accepts only the unit (Celsius or kelvin) you specify.
About ampere units: In Mastering Chemistry, answers in amperes must be coded in both A and amp. Use A for the first answer listed. However, for Mastering Physics and Mastering Engineering, amp is not considered correct—use only A for these disciplines.

Wrong-answer feedback: Add/delete (Optional)

Although optional, it is recommended that you provide wrong-answer feedback. Wrong-answer feedback can help students learn from their mistakes or incorrect choices.
Mastering provides the initial feedback "Incorrect; Try Again", followed by the follow-up text.
Example of wrong-answer feedback in student view (Standard View)
Important: Before evaluation, the numeric portion of wrong answer responses truncate to the default 3 significant figures—regardless of the significant figures format selected for the correct answer. Note that you can reset the answer format in wrong answer responses. To reset the answer format in wrong answer responses, see step 3 below.
You can enter one or more wrong-answer responses.
Example of wrong-answer feedback area in the Simple Editor for numeric value with units answers
Important: Before evaluation, the numeric portion of wrong answer responses truncate to the default 3 significant figures—regardless of the significant figures format selected for the correct answer. Note that you can reset the answer format in wrong answer responses. To reset the answer format in numeric wrong answer responses, see step 2 below.

Add wrong answer-feedback for the numeric with units answer type:

Select the add wrong-answer feedback link.
Enter wrong answers for the Number and Units boxes in the column "If student gives this answer".
- Grading tolerance —
  For each numeric wrong answer term, accept or change the default 2.00% Tolerance (acceptable variation or rounding error) that will trigger the associated wrong answer response. When the Format box is blank, the default value of 3 significant figures is in effect; only enter a value if you want to change this default value.
- Entering units for a wrong answer —
  Enter the units according to accepted units. Select the Preview link to view the rendered units expression in a different box.
- Empty Number text box —
  To add a wrong answer response for incorrect units when you aren't concerned about the associated numeric value, leave the Number box blank.
Enter your wrong answer feedback in the Show this response box, entering more specific ones first. Use your keyboard and options from the editing toolbar and menus.
To enter TeX in answer feedback, enter the TeX code, select it, and then choose TeX (or choose TeX and then enter your TeX). The unrendered TeX is highlighted in yellow.
Add a link to a hint in a wrong answer-response. (Optional)
Select add response to generate additional rows for as many wrong answers and associated wrong-answer feedback as you need. If you do enter additional wrong answer feedback, enter the more specific ones first.
Example of more specific order
If you want a wrong answer response to appear if students enter J for joules, but want a different response if students enter 10.5 J, the more specific wrong answer should appear first; “10.5 J” should precede “J” in the list of wrong answer responses.
To reorder wrong-answer responses — Select the Move Up or Move Down arrows to reorder the wrong answers and associated feedback.
To delete wrong-answer responses — Select Delete choice in the row for the response.
To check your edits without saving, select Validate (from the top toolbar) to verify the XML.
To save your edits, select Save (from the top toolbar) or the Save & Preview link (top right). Do NOT press Ctrl+S (Windows) or Command-S (Mac OS).
Test the student experience of wrong-answer feedback by submitting different incorrect answers in the saved item.

To delete wrong answer feedback — Select Delete on the toolbar for the response.

Follow-up text: Add/delete (Optional)

Follow-up text appears after a student completes a part question, whether the student answers correctly, exhausts all answer attempts, or requests the answer. Follow-up text can reinforce learning by providing more information or an interpretation of the answer the student just submitted.

Select the add follow-up text link.
Enter your answer feedback, using your keyboard and options from the editing toolbar and menus.

To delete follow-up text — Select the remove follow-up link.