# Grading tolerance and significant figures

Updated 15 Sep 2023

Both of these can affect whether mathematical answers are graded as correct or incorrect in Mastering assignments. How grading works

For grading purposes, some numeric answers to questions need to be exact. For example, the answer to the question "How many days are in a week?" must be **7**.

Other numeric answers may be graded as correct not only when they match the official Mastering answer, but also if they fall within an acceptable range of this official correct answer. This range is known as the **grading tolerance**.

"How many days are in a year?" The official answer is 365.24 days, but since a calendar contains 365 days, Mastering also considers this as correct because it's within the grading tolerance. (For more detailed examples, see the Examples section below.)

**The typical grading tolerance for most numeric answers in Mastering assignment questions is within 2% or 3%.**This means your answer can be plus or minus this percent of the correct answer. For example, if the grading tolerance is 2% and the correct answer is 100, then answers within the range of 98 and 102 are also graded as correct.**When your answer doesn't match the official correct answer in Mastering but is within the grading tolerance, your answer is accepted as correct.**

The answer feedback displays the answer you entered with a message saying that if you need this result for any later calculation in this assignment item you should keep all the digits during your initial calculations and round only as the final step before submitting your answer. This can avoid rounding errors that might cause your final answer to be out of the grading tolerance.

Significant figures (also known as *significant digits*) refer to the number of digits that are meaningful in weighing the accuracy of your answer compared to the official Mastering answer.

**Use at least 3 digits or significant figures in your answers**, unless otherwise specified or unless the exact answer can be expressed using fewer than 3 significant figures. If higher precision is required, or lower precision is allowed, this will be specified in the question or its instructions.*When you need to do multiple calculations to get an answer:***Use more significant figures than required during each calculation and round at the end only.**(Rounding too early can cause your final answer to be outside of the allowed tolerance range, even if you have otherwise calculated correctly!)

A question asks that you determine the area of a rectangle with sides of length L and width W. The area is the product of the length and the width (that is, area = L x W).

If length = | If width = | Minimum number of significant figures required in answer | Mastering official correct answer for Area (L x W) | Grading tolerance | Range of correct answers |
---|---|---|---|---|---|

8.40 |
1.50 |
3 |
12.6 |
3% |
12.3 - 12.9 |

26.0 |
8.00 |
3 |
208 |
2% |
204 - 212 |

26 |
8.0 |
2 |
210 |
2% |
206 - 214 |

20. |
5.0 |
2 |
100 |
3% |
97 - 103 |