Significant Figures & Numeric Answer Guidelines

Created by Harmony Taylor, Modified on Thu, Apr 30 at 9:49 AM by Harmony Taylor

Overview

In Expert TA, numeric answers are accepted if they meet either of the following criteria:

Within ±3% of the correct answer
Correct to at least two significant figures

General Rules

Avoid Premature Rounding

Do not round intermediate results if they will be used in subsequent calculations.
Rounding too early can introduce errors that affect the final answer.

Final Answer Requirements

Final answers must include at least two significant figures
Maintain full precision throughout calculations and round only at the end

Worked Example: Impact of Rounding

Correct answer: 0.7653

Case A – Correct Handling (Accepted)

Calculation:

(22.75 × cos(19) − 8.5) / 17

= (22.75 × 0.9455 − 8.5) 17

= (21.51 − 8.5) 17

= 13 17

= 0.76

Status: Accepted

Percent error: −0.69%
Correct to 2 significant figures: Yes
Within ±3% tolerance: Yes

Case B – Incorrect Rounding (Not Accepted)

Calculation:

(22.75 × cos(19) − 8.5) / 17

= (22.75 × 0.9455 − 8.5) 17

≈ (21 − 8.5) 17 ← rounded too early

= 12.5 17

= 0.74

Status: Not Accepted

Percent error: −3.31%
Correct to 2 significant figures: No
Within ±3% tolerance: No

What Went Wrong?

In Case B, the intermediate value 22.75 × 0.9455 = 21.51 was incorrectly rounded to 21. This introduced significant error in the final result.

Best Practices

Keep full precision during all intermediate steps
Only round the final answer
Ensure both significant figure and tolerance requirements are met
Use calculator tools when possible to avoid rounding errors

Key Takeaway

Small rounding differences can change correctness. Always preserve precision until the final step.