Scientific Measurements – Exam Review

Accuracy vs. Precision

• Accuracy: closeness of a measurement to the true/accepted value.
• Precision: closeness of repeated measurements to each other.
• Possible combinations: high-precision/low-accuracy, high-accuracy/low-precision, both high, or both low.

Significant Figures (Sig Figs)

  1. All non-zero digits are significant.

  2. Zeros between non-zero digits are significant.

  3. Leading zeros (left of first non-zero) are NOT significant.

  4. Trailing zeros to the right of a decimal are significant.

  5. Trailing zeros in whole numbers are ambiguous—use scientific notation to clarify.
    • Multiplication/Division → result keeps the smallest # of sig figs.
    • Addition/Subtraction → result keeps the least # of decimal places.
    • Rounding: if digit dropped > 5 → add 1; if < 5 → keep; if = 5 → add 1 only when last retained digit is odd.

Scientific Notation

• Format: N×10yN \times 10^{y} where 1\le N<10.
• Move decimal left → yy positive; move right → yy negative.
• Facilitates clear sig-fig reporting and handling very large/small values.

SI Base Units & Common Prefixes

• Base: meter (m), kilogram (kg), second (s), ampere (A), kelvin (K), mole (mol), candela (cd).
• Prefixes: tera (T, 101210^{12}), giga (G, 10910^{9}), mega (M, 10610^{6}), kilo (k, 10310^{3}), deci (d, 10−110^{-1}), centi (c, 10−210^{-2}), milli (m, 10−310^{-3}), micro (μ\mu, 10−610^{-6}), nano (n, 10−910^{-9}), pico (p, 10−1210^{-12}).

Derived Units: Volume & Density

• Volume: 1 m3=1000 L;  1 mL=1 cm31\,\text{m}^3 = 1000\,\text{L};\;1\,\text{mL}=1\,\text{cm}^3.
• Density: d=mVd = \dfrac{m}{V}; common lab unit g/cm3\text{g/cm}^3.
• Specific gravity = ratio of substance density to water density (unit-less).
• Float vs. sink: object floats if d<em>objectfluidd<em>{object}{fluid}.

Temperature Scales

• Celsius (∘C^\circ \text{C}), Kelvin (K), Fahrenheit (∘F^\circ \text{F}).
• Conversions:
TF=95TC+32T{\text{F}} = \frac{9}{5}T{\text{C}} +32
TC=59(TF−32)T{\text{C}} = \frac{5}{9}(T{\text{F}} -32)
TK=TC+273.15T{\text{K}} = T{\text{C}} + 273.15

Dimensional Analysis (Factor-Label)

• Set-up: quantity sought=given×∏conversion factors\text{quantity sought} = \text{given} \times \prod \text{conversion factors}
• Ensure units cancel algebraically; the remaining unit is the answer’s unit.
• Reliable for multi-step conversions (e.g., h→ms\text{h} \rightarrow \text{ms}, cm3→kg\text{cm}^3 \rightarrow \text{kg} via density).

Quick Reference: Measurement Skills

• Always read to one digit beyond the smallest scale division (estimated digit).
• Report answers with proper sig figs, correct unit, scientific notation when helpful.
• Check reasonableness: compare density, magnitude, or unit to known standards.