Lecture_2_-_sig_figs__dimensional_analysis

Chapter R: Uncertainty in Measurements, Significant Figures, and Dimensional Analysis

Course Guidelines

• Check Canvas site for syllabus and course policy documents.

• Read through course material and complete missed assignments to stay on track.

Office Hours

• Office hours:

  • Mondays 12:30-2:00 pm

  • Wednesdays 10:00-11:30 am

Uncertainty in Calculation

• Example problem:

  • Mass of porcelain spoon = 12.4303 g

  • Initial water volume = 68.0 mL, final volume = 73.1 mL

  • Density calculation: Density = mass/volume(5.1 mL).

Measurement Fundamentals

• Measurements must include both a number and a unit.

• All measurements have associated uncertainties (assumed ±1 in last digit).

• Precision: Closeness of measurements to each other.

• Accuracy: Closeness to true or accepted value.

Fundamental SI Units

• Mass: kg

• Length: m

• Time: s

• Temperature: K

• Electric current: A

• Amount of substance: mol

• Luminous intensity: cd

SI System Prefixes

• Common prefixes:

  • kilo (k) = 10^3

  • mega (M) = 10^6

  • giga (G) = 10^9

• Additional prefixes: pico (p), nano (n), etc.

Significant Figures

• Reflects measurement uncertainty.

• More digits = less relative uncertainty.

• Rules for counting:

  • Nonzero integers are significant.

  • Leading zeros are not significant.

  • Trailing zeros are significant if there's a decimal.

• Exact numbers (e.g., definitions) have infinite significant figures.

Significant Figures in Calculations

• Usually maintain one extra significant figure in intermediate calculations.

• Rounding rules apply at the end of the calculation.

Dimensional Analysis

• Focuses on unit cancellation in calculations.

• Uses unit factors for conversions, e.g., 1 in = 2.54 cm.

Example Problems

• Density problem with pennies (15 lb total, density 7.17 g/cm³).

• Floating/Sinking calculation for a 5.25 oz ball with diameter 2.9 in.