**Percent Differences**:

**Magnitude Difference**:

Percent Difference=∣F3,exp−F3,calc∣F3,exp+F3,calc2×100Percent Difference=2*F*3,exp​+*F*3,calc​​∣*F*3,exp​−*F*3,calc​∣​×100

**Angle Difference**:

Percent Difference=∣θ3,exp−θ3,calc∣θ3,exp+θ3,calc2×100Percent Difference=2*θ*3,exp​+*θ*3,calc​​∣*θ*3,exp​−*θ*3,calc​∣​×100

It seems there was some confusion in your formula formatting. Let's clarify and present the correct formulas for calculating percent differences between experimental and calculated values.

### 1. **Magnitude Percent Difference**:

The correct formula for calculating the percent difference between the experimental and calculated magnitudes is:

\[
\text{Percent Difference} = \frac{\left| F_{3,\text{exp}} - F_{3,\text{calc}} \right|}{\frac{F_{3,\text{exp}} + F_{3,\text{calc}}}{2}} \times 100
\]

This formula compares the experimental value \( F_{3,\text{exp}} \) with the calculated value \( F_{3,\text{calc}} \) and gives the difference as a percentage relative to their average.

### 2. **Angle Percent Difference**:

For the angle percent difference, the formula is similar:

\[
\text{Percent Difference} = \frac{\left| \theta_{3,\text{exp}} - \theta_{3,\text{calc}} \right|}{\frac{\theta_{3,\text{exp}} + \theta_{3,\text{calc}}}{2}} \times 100
\]

Here, \( \theta_{3,\text{exp}} \) is the experimental angle, and \( \theta_{3,\text{calc}} \) is the calculated angle (in degrees). The percent difference measures how much the experimental angle deviates from the calculated one.

### Follow-up Questions:

1. How can we reduce the percent difference between experimental and calculated magnitudes?
2. What factors can lead to discrepancies between the calculated and experimental angle values?
3. Why do we use the average in the denominator when calculating percent differences?
4. How do experimental errors propagate through these calculations?
5. How can you verify if your experimental setup is properly aligned with the calculated values?

**Tip**: When calculating percent differences, be careful with unit consistency (e.g., degrees vs. radians) and ensure accurate measurements to reduce error.

Explore how to calculate percent differences between experimental and calculated values. Learn the formulas and methods used to quantify deviations in magnitudes and angles. Suitable for advanced mathematics enthusiasts and researchers.

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