Metric System, Unit Conversions, and Density

Overview of Measurement Systems

  • Three systems of units:

    • English system

    • Metric system

    • International System of Units (SI)

  • Example conversions:

    • Pounds to kilograms

  • Importance of significant figures in calculations

Metric System

  • Base Units:

    • Volume: Liter (L)

    • Length: Meter (m)

    • Mass: Gram (g)

  • Prefixes:

    • Kilo- (k): 1000 times the base unit

    • Deci- (d): 10 times smaller than the base unit

    • Centi- (c): 100 times smaller than the base unit

    • Milli- (m): 1000 times smaller than the base unit

    • Micro- (µ): 1 million times smaller than the base unit

Conversion of Volume Units

  • Volume conversion:

    • 1 milliliter (mL) = 1 cubic centimeter (cm³)

    • 1 liter = 1000 mL = 1 cubic decimeter (dm³)

Conversion Factors

  • Definition of conversion factors: Ratios between two different units that express the same quantity.

  • Examples of common conversion factors:

    • 1000 millimeters (mm) in a meter (m)

    • 1000 milligrams (mg) in a gram (g)

Converting Units

Example: Convert liters to milliliters

  • Given: 0.0500 L, to convert to mL

  • Set up:

    • 0.0500 L × (1000 mL / 1 L)

  • Calculation:

    • [Number of significant figures] - final result has 3 significant figures

    • Result: 50.0 mL

Important Relationships to Memorize

  1. 1 m = 1000 mm

  2. 1 kg = 1000 g

  3. 1 L = 1000 mL

  4. 1 kg = 2.2 lbs

  5. 1 lb = 16 oz

Example Conversions: Pounds to Grams

Calculation Process for 30.4 lbs to grams

  1. Determine conversion factors:

    • 2.2 lbs = 1 kg

    • 1000 g = 1 kg

  2. Set up the calculation:

    • 30.4 lbs × (1 kg / 2.2 lbs) × (1000 g / 1 kg)

  3. Ensure unit cancellation:

    • lbs cancels with lbs, kg cancels with kg

    • Resulting unit = g

  4. Calculate and round:

    • Result rounded to 3 significant figures: 13800 g

Word Problems and Multiple Conversions

  1. Identify what you have, what you need, and the conversion factors

  2. Example Problem: Dosage Calculations

    • Given weight in pounds, needs conversion to kg for medication dosing

    • Use known conversion factors for units

  3. Example Problem: Recipe Conversions

    • Given volume in liters, convert to cups

    • Use conversion factors: 1 L = 1.057 quarts, 1 quart = 4 cups

Density and Its Calculation

  • Density Definition: Mass per unit volume

  • Formula: Density (d) = Mass (m) / Volume (V)

  • Calculating Density:

    • Find mass using a balance

    • Find volume using water displacement for irregular objects

  • Example:

    • Initial Volume: 6.6 mL, Final Volume: 7.5 mL

    • Mass of object: 8.064 g

  • Volume of object = Final Volume - Initial Volume = 7.5 mL - 6.6 mL = 0.9 mL

  • Density = 8.064 g / 0.9 mL = 8.96 g/mL (round to 2 significant figures = 9.0 g/mL)

Specific Gravity

  • Specific Gravity = Density of substance / Density of water

  • Example Calculation: If density of urine is 1.03 g/mL,

    • Specific gravity = 1.03 (no units)

    • Specific gravity of 2.0 implies density of 2.0 g/mL

Practical Applications

  • Significant figures in medical calculations are critical

  • Rounding and conversion accuracy are essential for patient safety

  • Understanding volume dosing and medication management is crucial

Summary

  • Solid grasp of metric system, conversion factors, and significant figures are essential skills

  • Research and practice word problems and conversion tasks

  • Be prepared for practical applications in healthcare settings where precise calculations can impact patient care.