Approximations

Definition

Approximations are simplified representations or calculations that are close to the exact value, used when exact values are impractical. They help in making complex problems more manageable.

5 Must Know Facts For Your Next Test

1. Approximations are essential for dealing with real-world measurements where precision is limited by instruments.
2. A common method of approximation in physics is using significant figures to limit the precision of a number.
3. Approximations can introduce errors, which must be understood and minimized for accurate results.
4. Linear approximations can be used to simplify complex functions near a point of interest, often referred to as linearization.
5. The small-angle approximation ($\sin(\theta) \approx \theta$ when $\theta$ is small) is frequently used in physics problems.

Review Questions

• Why are approximations important in physical measurements?
• What is the small-angle approximation and when is it applied?
• How do significant figures relate to approximations?

Related terms

Significant Figures: Digits in a number that contribute to its precision, indicating the accuracy of a measurement.

Error Analysis: The study of uncertainties in physical measurements and how they affect results.

Linearization: The process of approximating a nonlinear function by a linear function near some point.