Unit Conversions and Measurement (Video Notes)

Metric prefixes and unit conversion overview

• Prefix basics: micro (μ), milli (m), centi (c), deci (d) are shorthand for powers of ten. Common forms mentioned: μ, u, and in the medical field sometimes mc (for micro) as in mcg for micrograms. milli is denoted with m (e.g., mg, mm, mL).
• Important caution: milli uses an m that can be confused with meter (also m). For example, millimeter is written as mm, while meter is written as m.
• Quick rule of conversions: count the number of steps (powers of ten) you move the decimal between prefixes. The number of steps equals the difference in exponents, and direction depends on whether you’re moving to a larger or smaller unit.
• Example idea given in class: moving micro to centi involves 4 steps (from 10^{-6} to 10^{-2} is a difference of 4 orders of magnitude), so you move the decimal to the right by 4 places.
• Practical mental model shared: 54321 conversions (a mnemonic-like cue) to help remember the order of prefixes when doing quick checks.
• Example notes:
  • If you go from micro to centi, you move the decimal 4 steps to the right: 0.000123 → 1.23 × 10^? (illustrative, watch signs).
  • 27 decimeters to centimeters: 27 \, ext{dm} = 270 \, ext{cm}.
  • 170 cm tall converts to meters: 170 ext{ cm} = 1.7 ext{ m}.
• Common relations:
  • 1 L = 1000 mL.
  • 1 mL = 1 cm^3 = 1 cc.
  • 1 m = 100 cm = 1000 mm.
  • 1 cm = 10 mm.
• Practical note on reading measurements:
  • When reading scales, the increments depend on the instrument; beakers are for rough estimates; graduated cylinders are more precise; microliters (μL) and milliliters (mL) are common in lab tasks.

Reading the meter stick and reading scales

• Meter sticks have two sides: inches side (less relevant here) and the meter side with many centimeter and millimeter marks.
• Key reading rule: the major lines with numbers denote centimeters; between each centimeter there are 10 tiny lines, which are millimeters.
• Quick conversions on the stick:
  • Each centimeter mark is a full centimeter.
  • Each small hash (between centimeter marks) is a millimeter. There are 10 millimeters per centimeter:
    {1 ext{ cm}} = 10 ext{ mm}.
• Reading strategy when measuring length: alignment of the starting point and end point, with attention to where the decimal would be placed in your measurement. (The class discussion included examples like 55 cm as a position on the stick.)
• Note on precision: some sticks show full numbers only on the centimeter marks; others have all marks (with millimeters) labeled.

Volume measurement: beakers, graduated cylinders, and menisci

• Beakers: useful for stirring and rough volume estimates; not highly precise.
  • Accuracy boxes or labels often show approximate volumes; not ideal for precise measurements.
  • When pouring, read at the bottom of the meniscus only for liquids like water (the true volume is where the bottom of the meniscus sits).
• Graduated cylinders: tall, thin tubes with finer graduations; designed for accurate volume measurements.
  • How to read: count the markings between lines. If there are many lines between two labeled marks, each small division represents a smaller increment (e.g., 0.1 mL or 0.2 mL depending on the instrument). Some cylinders have more finely spaced lines (so each line could represent 0.1 mL, 0.05 mL, etc.). Always check what each division represents on your specific cylinder.
• Meniscus: the curved surface of a liquid in a container, due to adhesion; read at the bottom of the meniscus for accuracy when measuring liquids like water.
• Volume conversion examples discussed:
  • 50 mL in a beaker, then transferred to a graduated cylinder to read precisely.
  • Reading the scale: if there are 9 lines between marks, each line may represent 1 mL; if there are 4 lines between marks, each line may represent 0.5 mL or another increment (depends on the instrument). Always verify your specific instrument’s increment.
• Archimedes' principle (introducing displacement): volume of a solid can be determined by water displacement in a graduated cylinder.
  • Procedure described: fill a cylinder with 50 mL of water, gently lower a solid object into the water, and read the new volume. The volume of the object is the difference:
    V{ ext{object}} = V{ ext{final}} - V_{ ext{initial}}.
  • Practical notes: don’t spill or lose water; keep water in the cylinder and subtract the initial volume from the final volume after immersion.
• Transfer pipettes vs micropipettes:
  • Transfer pipettes: disposable bulbs used to move measured volumes; you can read the top line and estimate volumes with the bulb; typical marks roughly correspond to 0.5 mL, 1 mL, etc., and you can draw up to a target and release to hit the mark.
  • Micropipettes: more precise, measure in microliters (µL), typically with ranges like 20–200 µL or 100–1000 µL; set the volume using the dial to a middle of the range, then use the first stop to draw and the second stop to dispense.
  • Handling tips: attach a disposable pipette tip securely; don’t draw liquid without a tip; eject tips into designated waste boxes.
• Practical procedure tips given in class:
  • Use the transfer pipette to measure roughly and then adjust by slowly releasing to hit exact marks.
  • For micropipettes, hold the instrument with the thumb on the plunger, place the tip in the liquid, press to the first stop to draw, then to the second stop to dispense; tips eject into waste boxes.

Archimedes principle and density concepts

• Archimedes principle summary: the buoyant force on an object submerged in a fluid equals the weight of the fluid displaced by the object; used to measure volume by displacement.
• Density and buoyancy basics:
  • Density is a measure of how closely packed the molecules are in a substance.
  • If the density is equal to that of water (about 1 g/mL at room temperature), the object will have neutral buoyancy in water.
  • If density > 1 g/mL, the object tends to sink in water; if density < 1 g/mL, it tends to float.
  • Density formula (basic):
    
    ho = rac{m}{V}.
• Specific gravity (SG): a dimensionless ratio comparing the density of a substance to the density of a reference material (usually water at 1 g/mL at room temperature).
  • Definition used in class: SG = rac{
    ho}{
    ho_{ ext{ref}}}.
  • For water as the reference (ρ_ref ≈ 1 g/mL), SG ≈ ρ, so SG equals density when comparing to water.
• Common equivalences:
  • 1 cubic centimeter (cc) = 1 cubic centimeter = 1 mL: 1 ext{ cc} = 1 ext{ mL}.
  • 1 mL = 1 cm^3; thus, density in g/mL can be used directly with volumes in mL to determine buoyancy.

Scientific notation: building and converting numbers

• Why we use scientific notation: it makes very large and very small numbers easy to compare and work with, especially in science where orders of magnitude matter.
• Format: N = c imes 10^{e} where the coefficient c satisfies 1
  leq c < 10 and e is an integer.
• Building numbers into scientific notation (rules from class):
  • Start from the left, find the first nonzero digit, and place a decimal immediately after that digit to form the coefficient.
  • The exponent e is the number of places the decimal point moved to produce that coefficient from the original number. Positive if moving left (to create a larger number), negative if moving right (to create a smaller number).
• Example 1 (from the lecture): convert 0.00215. The first nonzero digit is 2; the decimal moves 3 places to the right to place the decimal after 2, giving a coefficient of 2.15. The number of moves is 3, so the exponent is -3:
  0.00215 = 2.15 imes 10^{-3}.
• Example 2 (from the lecture): convert 3.51 × 10^4 back to standard form. The decimal point moves 4 places to the left to yield 35100 in ordinary notation (the lecture noted 35,000 as an approximation; the exact value is 35,100).
  • Rule: to convert from scientific notation to standard form, move the decimal point to the left by e places if e is positive; to the right by |e| places if e is negative.
• Practice approach described in class:
  • Build numbers from scratch using the coefficient between 1 and 10 and the exponent.
  • Then, for backward conversion, read the exponent and move the decimal appropriately, inserting zeros as needed.
• Common pitfalls discussed: leading decimal points (e.g., 0.144 as 0.144 or 0.0144) and ensuring proper placement of the decimal so the leading digit is nonzero.

Lab safety, logistics, and workflow notes from the class

• PPE and safety: goggles and gloves must stay on while equipment is out; goggles protect eyes from splashes; gloves protect hands from contact with lab materials.
• Equipment handling reminders:
  • When using goggles, ensure a secure seal; if you wear glasses, you can tilt and pull them over with a snug fit.
  • Alcohol wipes are available to clean goggles and gloves to remove germs, sweat, and makeup.
• Lab grouping and instructor interactions:
  • Students work in lab groups; each group may be assigned specific questions to present on the board.
  • The instructor moves around to assist, especially with groups that are struggling.
• Waste and cleanup:
  • Transfer pipette tips should be disposed of in appropriate boxes; micropipette tips are disposable.
  • After experiments, pour out or properly set aside water, dry equipment, and store safely.
• Quick safety reminders about lab etiquette and common-sense practices:
  • Do not mix up units and be careful when reading scales or reading the meniscus.
  • If a spill occurs, use paper towels located near sinks; keep workspace clean.

Quick synthesis: connecting the concepts to the workflow

• Tools and measurement literacy:
  • Distinguish between beakers (rough volumes) vs graduated cylinders (precise volumes).
  • Read the bottom of the meniscus for liquids like water to obtain accurate volumes.
  • Remember the cc and mL equivalence for solid vs liquid volumes: 1 cc = 1 mL.
• Mass, volume, and density:
  • Density is mass per unit volume:
    ho = rac{m}{V}. The density determines buoyancy (float vs sink) in a given fluid.
  • Specific gravity is a density comparison to water: SG = rac{
    ho}{
    ho{ ext{water}}} ext{ (with } ho{ ext{water}} ext{ ≈ } 1 ext{ g/mL)}. If comparing to water, SG ≈ ρ.
• Volume measurement via displacement:
  • Use water displacement to determine the volume of irregular objects: determine the difference between final and initial water volumes in a graduated cylinder: V{ ext{object}} = V{ ext{final}} - V_{ ext{initial}}.
• Scientific notation fluency as a foundational skill:
  • Build and convert numbers using the format N = c imes 10^{e}, with a clear understanding of how the coefficient and exponent relate to decimal placement and magnitude.
• Classroom practice takeaway:
  • Practice conversions between prefixes, lengths, volumes, and temperatures as you prepare for the exam, including common pitfalls with leading zeros and decimal placement.