convertion notes

Equality Statements and Conversion Factors

• Equality Statement: Two different units describing the same amount (e.g., $1 \text{ ft} = 12 \text{ in}$).

• Conversion Factor: A fraction derived from an equality used to switch units.

  • Examples:

  • $\frac{60 \text{ min}}{1 \text{ hr}}$ or $\frac{1 \text{ hr}}{60 \text{ min}}$

  • $\frac{1 \text{ m}}{100 \text{ cm}}$ or $\frac{100 \text{ cm}}{1 \text{ m}}$

• Labels: Scientists must include units with numbers for calculations to be meaningful.

Extracting Equivalence

• Rates: 85 km/h yields $\frac{85 \text{ km}}{1 \text{ hr}}$.

• Percentages: 18% body fat is $\frac{18 \text{ kg fat}}{100 \text{ kg total weight}}$.

• Ratios: Parts per million (mg/kg) and parts per billion ($\mu\text{g/kg}$).

Problem-Solving Steps

1. Identify Given (G) and Unknown (U).

2. Set up Conversions: Arrange factors so units cancel out, leaving the target unit.

3. Significant Figures: Conversion factors are exact. The final answer should match the significant figures of the Given value.

Examples

• Pounds to Kilograms:

  • $\frac{155 \text{ lb}}{1} \times \frac{1 \text{ kg}}{2.2 \text{ lb}} = 70.5 \text{ kg}$ (3 sig figs).

• Days to Minutes:

  • $1.35 \text{ days} \times \frac{24 \text{ hr}}{1 \text{ day}} \times \frac{60 \text{ min}}{1 \text{ hr}} = 1940 \text{ min}$ (Adjusted to 3 sig figs).

• Medication Dosage:

  • Convert 0.150 mg to $\mu\text{g}$: $0.150 \text{ mg} \times \frac{1000 \ \mu\text{g}}{1 \text{ mg}} = 150 \ \mu\text{g}$.

  • Convert to tablets (75 $\mu\text{g}$ per tablet): $\frac{150 \ \mu\text{g}}{75 \ \mu\text{g/tablet}} = 2 \text{ tablets}$.

Real-World Application

• LD50 (Lethal Dose): Calculated by multiplying body mass (kg) by the toxicity ratio (e.g., 192 mg/kg for caffeine) to determine safe exposure limits.