Chapter 1 - Prefixes and SI Units

Metric prefixes and SI unit basics

• Purpose: Understand prefixes used in the metric system and SI units, plus basic unit conversions and applications.

Prefix table (Table 1.4): Prefixes Used in the Metric System and with SI Units

• Prefix: Peta; Abbreviation: P; Meaning: 10^{15}; Example: 1 petawatt (PW)
• Prefix: Tera; Abbreviation: T; Meaning: 10^{12}; Example: 1 terawatt (TW)
• Prefix: Giga; Abbreviation: G; Meaning: 10^{9}; Example: 1 gigawatt (GW)
• Prefix: Mega; Abbreviation: M; Meaning: 10^{6}; Example: 1 megawatt (MW)
• Prefix: Kilo; Abbreviation: k; Meaning: 10^{3}; Example: 1 kilowatt (kW)
• Prefix: Deci; Abbreviation: d; Meaning: 10^{-1}; Example: 1 deciwatt (dW)
• Prefix: Centi; Abbreviation: c; Meaning: 10^{-2}; Example: 1 centiwatt (cW)
• Prefix: Milli; Abbreviation: m; Meaning: 10^{-3}; Example: 1 milliwatt (mW)
• Prefix: Micro; Abbreviation: μ; Meaning: 10^{-6}; Example: 1 microwatt (μW)
• Prefix: Nano; Abbreviation: n; Meaning: 10^{-9}; Example: 1 nanowatt (nW)
• Prefix: Pico; Abbreviation: p; Meaning: 10^{-12}; Example: 1 picowatt (pW)
• Prefix: Femto; Abbreviation: f; Meaning: 10^{-15}; Example: 1 femtowatt (fW)
• Prefix: Atto; Abbreviation: a; Meaning: 10^{-18}; Example: 1 attowatt (aW)
• Prefix: Zepto; Abbreviation: Z; Meaning: 10^{-21}; Example: 1 zeptowatt (zW)

Notes:

• The watt (W) is the SI unit of power, which is the rate at which energy is either generated or consumed.
• The SI unit of energy is the joule (J); 1 J = 1 kg·m^2/s^2 and 1 W = 1 J/s.
• Greek letter mu (μ) is pronounced "mew".

Basic unit relationships (context from the transcript)

• Power: W = \dfrac{J}{s}
• Energy: J = \mathrm{kg}\cdot \mathrm{m}^2/\mathrm{s}^2

Quick practice questions from Page 3 (with answers)

• (a) The unit that equals 10^{-9} gram is a nanogram: 1\text{ ng} = 10^{-9}\text{ g}
• (b) The unit that equals 10^{-6} second is a microsecond: 1\text{ μs} = 10^{-6}\text{ s}
• (c) The unit that equals 10^{-3} meter is a millimeter: 1\text{ mm} = 10^{-3}\text{ m}
• (b) How many picometers are there in 1 m?
  • Since 1 pm = 10^{-12} m, there are 1\text{ m} = 10^{12}\text{ pm}
• (c) Express 6.0 × 10^{3} m using a prefix to replace the power of ten:
  • 6.0 × 10^{3} \text{ m} = 6.0\text{ km}
• (d) Use exponential notation to express 4.22 mg in grams:
  • 4.22\text{ mg} = 4.22 × 10^{-3}\text{ g}
• (e) Use decimal notation to express 4.22 mg in grams:
  • 4.22\text{ mg} = 0.00422\text{ g}

Doing prefix conversions (conceptual overview)

• A prefix is a conversion factor; you can treat prefixes as powers of ten when converting units.
• Example relation used in the transcript: 1 mg = 1 × 10^{-3} g.
• A common exercise: Convert among mg, g, pg, etc., using their fixed relationships:
  • 1 g = 10^{3} mg
  • 1 mg = 10^{3} μg
  • 1 g = 10^{12} pg
• Example calculation shown in the transcript (12.3 mg to pg):
  • 1 mg = 10^{9} pg
  • Therefore, 12.3\text{ mg} = 12.3 × 10^{9} \text{ pg} = 1.23 × 10^{10} \text{ pg}
  • Also note a recommended notation for scientific format: use x × 10^{n} rather than mixed forms.

Prefix conversions with a practical example: density and volume

• Given the density of Hg: \rho = 13.6\;\frac{g}{mL}
• Question: What volume (mL) of Hg is 110 g?
• Solution:
  • Volume formula: V = \dfrac{m}{\rho}
  • V = \dfrac{110\;\text{g}}{13.6\;\frac{g}{\text{mL}}} = 8.088…\;\text{mL}
  • Report with appropriate significant figures. If 110 g is treated as having two or three significant figures (depending on context), you might present as ~8.09 mL (3 s.f.) or 8.1 mL (2 s.f.).

Pace and distance: unit conversions (Page 6 context)

• Common conversion factors:
  • 60\;\text{s} = 1\;\text{min}
  • 1\;\text{mile} = 1.60934\;\text{km}
  • 1\;\text{km} = 10^{3}\;\text{m}
• Usage:
  • If you know pace in s/m, you can convert to other pace/distance units using these relationships.
  • Example approach: convert all values to base units (s, m) first, then switch to target units using the above factors.

Temperature conversions (31°C example)

• Given: 31°C
• Kelvin: TK = TC + 273.15 = 31 + 273.15 = 304.15\text{ K}
• Fahrenheit: TF = TC \times \frac{9}{5} + 32 = 31 \times 1.8 + 32 = 87.8\,^{\circ}\text{F}
• Answers: 304.15\text{ K}, \; 87.8\,^{\circ}\text{F}

Significant figures practice (Page 8)

• Number of significant figures:
  • (a) 4.003 → 4 s.f.
  • (b) 6.023 × 10^{23} → 4 s.f. (the mantissa 6.023 has four digits)
  • (c) 5000 → ambiguous; commonly interpreted as 1 s.f. unless otherwise indicated (e.g., 5000. has 4 s.f. or 5.000 × 10^3 would denote 4 s.f.). For a measured quantity, treat as 1 s.f. unless specified.
• Box volume example:
  • Dimensions: 15.5 cm, 27.3 cm, 5.4 cm
  • Volume: V = 15.5 \times 27.3 \times 5.4 = 2285.01\;\text{cm}^3
  • Sig figs: smallest factor has 2 s.f. (5.4 has 2 s.f.), so final should be reported as 2.3 \times 10^{3}\;\text{cm}^3 or 2300 cm^3 (depending on required precision).

Dimensional analysis practice (Page 9 conversions)

• Problem set: 1) Convert 1.234 mg to dg:
  • 1 mg = 10^{-3} g
  • 1 g = 10 dg (since 1 dg = 0.1 g)
  • Therefore, 1 mg = 10^{-3} g = 0.001 g = 0.01 dg
  • So, 1.234 \text{ mg} = 0.01234 \text{ dg}
    2) Convert 0.490 × 10^{-3} A to GA (giga-ampere):
  • 0.490 × 10^{-3} A = 4.90 × 10^{-4} A
  • 1 GA = 10^{9} A
  • So, 4.90 × 10^{-4} \text{ A} = 4.90 × 10^{-13} \text{ GA}
    3) Convert 710 m to nm:
  • 1 m = 10^{9} nm
  • So, 710 \text{ m} = 7.10 × 10^{11} \text{ nm}
    4) Convert 0.321 mm/min to ft/hr (with 1 m = 3.281 ft):
  • 0.321 mm = 0.321 × 10^{-3} m = 3.21 × 10^{-4} m
  • per hour: multiply by 60 min/hr: 3.21 × 10^{-4} × 60 = 0.01926 \text{ m/hr}
  • Convert to ft/hr: 0.01926 \text{ m/hr} × 3.281 \frac{\text{ft}}{\text{m}} ≈ 0.0632 \text{ ft/hr}
  • Final: 6.32 × 10^{-2} \text{ ft/hr}

Additional notes and clarifications

• The transcript includes several OCR/typo issues (e.g., misrendered symbols and garbled words). The corrected, standard SI interpretations above are used for the notes:
  • Micro symbol is the Greek mu: \mu, not a Latin 'u'.
  • Standard prefix symbols: P, T, G, M, k, d, c, m, μ, n, p, f, a, Z (for zepto) with exponents as listed.
• When performing calculations with prefixes, treat them as powers of ten and carry through with the appropriate significant figures from the original measurements.
• The notes here reflect the content and typical expectations from the material in the transcript; if you have access to the original slides or textbook, use them to confirm any ambiguities in the garbled sections.