Notes for Unit Conversions and Dosage Calculations

1 kilogram equals 2.205 pounds
- Expressed as a conversion: $1\ \text{kg} = 2.205\ \text{lb}$
16 quarts to liters
- You start from an American (US customary) measurement and convert to metric
- Conversion shown below:
- Calculation: $16\ \text{qt} \times \frac{0.946353\ \text{L}}{1\ \text{qt}} = 15.141648\ \text{L} \approx 15.1416\ \text{L}$
26.2 miles to kilometers
- 1 mile ≈ 1.60934 km
- Calculation: $26.2\ \text{mi} \times 1.60934\ \frac{\text{km}}{\text{mi}} = 42.164708\ \text{km} \approx 42.1647\ \text{km}$
Understanding conversion factors
- Look at the tables on your conversion sheet (e.g., “table two” mentioned in the transcript)
- Make sure you understand how the conversion factor was derived from those tables
Practical reminder
- When doing conversions, verify which system is being used and check your conversion sheet for the correct factors
Questions to consider
- “What is the starting unit (USC or USCS)?”
- “Is the target unit metric or imperial?”

The Celsius scale facts used in the transcript
- Water freezes at 0°C
- Water boils at 100°C
Kelvin basics
- Kelvin is an absolute scale; to convert from Celsius:
- $K = C + 273.15$
- Example: if C = 15, then $K = 15 + 273.15 = 288.15\ \text{K}$
Celsius to Fahrenheit conversion
- The transcript states: multiply by 1.8 (or 9/5) and then add 32
- Formula: $F = \frac{9}{5} \cdot C + 32 = 1.8\cdot C + 32$
- Example: for C = 15, $F = \frac{9}{5}\cdot 15 + 32 = 59^\circ\text{F}$
Fahrenheit to Celsius (inverse, if needed)
- Formula: $C = \frac{F - 32}{1.8}$
Order of operations reminder
- Multiplication comes before addition, so in expressions like $F = 1.8\cdot C + 32$ there is no need for extra parentheses
Calculator tip
- Practice entering Celsius to Kelvin and Fahrenheit conversions to verify the calculator’s results

Density (general concept)
- Density is mass per unit volume: $\rho = \frac{m}{V}$
- Common density units include $\text{kg/m}^3$ , $\text{g/cm}^3$ , etc.
Population density (a common applied density)
- Definition: number of people per unit area
- Significance: informs planning for police, EMS, hospitals, and other public services
- Why density matters in real-world planning: higher density can affect the need for public resources and infrastructure
Key takeaway
- Population density is the most commonly cited density in public planning; other densities (e.g., material density) use mass/volume units

Concept: concentration and dosage are based on mg per kg of body weight per day
- Typical formulation in the transcript: dosage based on a rate of 30 mg per kg of body weight per day, divided into multiple doses per day
Medical dosage example (amoxicillin)
- Patient: child weighing 15 kg
- Prescription: 30 mg per kg per day, divided into doses every 12 hours (i.e., 2 doses per day)
Step-by-step calculation
- Daily dose: $D_{\text{day}} = 30\ \frac{\text{mg}}{\text{kg}} \times m\quad\text{where } m = 15\ \text{kg}$
- Substitute: $D_{\text{day}} = 30\ \frac{\text{mg}}{\text{kg}} \times 15\ \text{kg} = 450\ \text{mg/day}$
- Doses per day: 2 (every 12 hours)
- Per-dose dose: $D<em>{\text{dose}} = \frac{D</em>{\text{day}}}{2} = \frac{450\ \text{mg}}{2} = 225\ \text{mg/dose}$
Suspension concentration problem
- Suspension concentration: $C = 25\ \frac{\text{mg}}{\text{mL}}$
- Volume per dose: $V = \frac{D_{\text{dose}}}{C} = \frac{225\ \text{mg}}{25\ \frac{\text{mg}}{\text{mL}}} = 9\ \text{mL/dose}$
Result for the dosage per administration
- The child should receive 9 mL per dose, every 12 hours (two times per day)
Formulas to remember (compact)
- Daily dose: $D_{\text{day}} = \left(30\ \frac{\text{mg}}{\text{kg}}\right) \times m$
- Per-dose: $D<em>{\text{dose}} = \frac{D</em>{\text{day}}}{n} \quad(n = \text{doses per day})$
- Volume: $V = \frac{D_{\text{dose}}}{C}$
Note on the reference sheet
- The sheet may not include temperature conversions; other conversions should be available

Impounded yard anecdote about costs and processes
Public transportation comparison and commentary on infrastructure
Discussion of DUI, public safety, and ethics
Statement: "the public good takes precedence" when balancing individual rights and safety
Note: These remarks are tangential to the math/chemistry content but are included here to reflect the transcript

Convert 1 kg to pounds: $1\ \text{kg} = 2.205\ \text{lb}$
Convert 16 quarts to liters: $16\ \text{qt} \times \frac{0.946353\ \text{L}}{1\ \text{qt}} = 15.141648\ \text{L} \approx 15.14\ \text{L}$
Convert 26.2 miles to kilometers: $26.2\ \text{mi} \times 1.60934\ \frac{\text{km}}{\text{mi}} = 42.164708\ \text{km} \approx 42.1647\ \text{km}$
Celsius to Fahrenheit example (from transcript): for C = 15, $F = \frac{9}{5} \cdot 15 + 32 = 59^\circ\text{F}$
Fahrenheit to Celsius (inverse) practice: $C = \frac{F - 32}{1.8}$
Additional reminder: keep track of units and the number of doses per day when calculating dosages