Metric System Study Notes

Today's Objectives

  • Convert between the Metric System and the US System (Calculator Questions)
  • Convert within the Metric System (Non-Calculator)
  • Memorize metric prefixes
  • Use metric system units to calculate length, area, volume, mass, and weight

Why conversions matter

  • Gas price example used to illustrate the practical importance of conversions: "BECAUSE! I was traveling this summer and found gas for 1.49. How good or bad of a deal was this?"
  • Within metric system conversions are needed in current/future science classes (chemistry, biology, physics) and future programs (nursing, rad-tech, ultrasound, etc).
  • Prefix usage by fields:
    • Rad-tech: milli, kilo, centi, mega, micro, likely others
    • Ultrasound: mega, centi, milli, kilo, micro, likely others
    • Nursing: milli, kilo, micro, likely others
  • We will practice as many of these prefixes as Activ allows.

Metric Prefix Scale basics

  • The mnemonic: KHDUDCM stands for the order of metric prefixes around the base unit:
    • Giga, Mega, kilo, (base unit), deci, centi, milli, with additional prefixes outside this range.
  • Expanded scale includes: giga (G), mega (M), kilo (k), (base unit), deci (d), centi (c), milli (m), micro (μ), nano (n), etc.
  • The standard scale also includes larger prefixes beyond giga (tera, peta, etc.) and smaller prefixes beyond nano (pico, femto, etc.).
  • The micro prefix uses the Greek letter μ to denote 10^{-6}.
  • The mnemonic is helpful but incomplete: "Great Mighty King Henry Died by Drinking Chocolate Milk Until Nine" expands to include giga, mega, micro, nano, etc. μ
  • All prefixes are associated with scientific notation (see section 5.2).

Prefix powers of ten (major prefixes and their values)

  • Giga, G: 10910^{9}
  • Mega, M: 10610^{6}
  • kilo, k: 10310^{3}
  • deci, d: 10−110^{-1}
  • centi, c: 10−210^{-2}
  • milli, m: 10−310^{-3}
  • micro, \mu: 10−610^{-6}
  • nano, n: 10−910^{-9}
  • (Note: the base unit corresponds to 10010^{0})

Tricks with prefixes and decimal movement

  • Each power of ten corresponds to moving the decimal point by one place per step.
    • Positive exponents (moving to larger units) move the decimal point to the right.
    • Negative exponents (moving to smaller units) move the decimal point to the left.
  • Examples:
    • Converting from MHz to Hz moves the decimal 6 places to the right: 1 MHz = 106 Hz10^6\,\text{Hz}.
    • Converting from nm to m moves the decimal 9 places to the left: 1 nm = 10−9 m10^{-9}\,\text{m}.
  • Quick intuition: a larger prefix means you’re talking about a larger unit; a smaller prefix means a smaller unit, so you divide when moving to a larger unit and multiply when moving to a smaller unit.

LENGTH

  • Standard unit: meter (m)
  • Frequently used units:
    • centimeter (cm): 1 cm=1100 m=0.01 m1\text{ cm} = \frac{1}{100}\text{ m} = 0.01\text{ m}
    • 100 cm = 1 m
    • kilometer (km): 1 km=1000 m1\text{ km} = 1000\text{ m}
    • millimeter (mm): 1 mm=11000 m=0.001 m1\text{ mm} = \frac{1}{1000}\text{ m} = 0.001\text{ m}
    • 1000 mm = 1 m, 10 mm = 1 cm

Conversions (practice items)

  • Convert between metric units:
    • 8500 cm→ m8500\ \text{cm} \to \ \text{m}
    • 5.3 km→ m5.3\ \text{km} \to \ \text{m}
    • 27,500 m→ km27{,}500\ \text{m} \to \ \text{km}

In-class conversions (notes from the slides)

  • In-class QUESTION #1 (content not provided in transcript)
  • In-class QUESTION #2 (content not provided in transcript)
  • In-class QUESTION #3 (content not provided in transcript)
  • In-class QUESTION #4 (content not provided in transcript)
  • In-class QUESTION #5 (content not provided in transcript)
  • In-class QUESTION #6 (content not provided in transcript)

VOLUME

  • 1 cubic centimeter (cc) = 1 cm × 1 cm × 1 cm = 1 mL
  • 1 L = 10 cm × 10 cm × 10 cm = 1000 mL
  • 1 mL = 1/1000 L
  • Related conversions:
    • 1 mL=1×10−3 L1\text{ mL} = 1\times10^{-3}\text{ L}
    • 1 L=103 mL1\text{ L} = 10^3\text{ mL}

VOLUME: Examples

  • Convert:
    • 8974 mL→ L=89741000=8.974 L8974\ \text{mL} \to \ \text{L} = \frac{8974}{1000} = 8.974\ \text{L}
    • 8.7 L→ mL=8.7×1000=8700 mL8.7\ \text{L} \to \ \text{mL} = 8.7 \times 1000 = 8700\ \text{mL}

MASS

  • Important concept: Mass does not equal weight
  • Mass relationships:
    • 1 kg=1000 g1\ \text{kg} = 1000\ \text{g}
    • Density note: mass of 1 L of water is approximately 1 kg (density ~1 g/mL)
    • 1 g=1000 mg1\ \text{g} = 1000\ \text{mg}

MASS: Conversions (examples)

  • Convert:
    • 5.2 kg→ g=5.2×103=5200 g5.2\ \text{kg} \to \text{ g} = 5.2 \times 10^3 = 5200\ \text{g}
    • 4.2 g→ kg=4.2×10−3=0.0042 kg4.2\ \text{g} \to \text{ kg} = 4.2 \times 10^{-3} = 0.0042\ \text{kg}

TEMPERATURE

  • Standard unit: degrees Celsius (C)
  • Formulas:
    • C=59(F−32)C = \dfrac{5}{9}(F - 32)
    • F=95C+32F = \dfrac{9}{5}C + 32

TEMPERATURE: Convert practice

  • Examples (to be computed):
    • 10∘C→F10^{\circ}\text{C} \to F
    • 10∘F→C10^{\circ}\text{F} \to C

UNIT CONVERSIONS (Metric ↔ US)

  • We will use provided conversion factors and calculator tools (Desmos) for calculator-based questions; you do not need to memorize every factor, but memorize a few commonly used ones.
  • Conversion factors overview (from Table 2 and Table 3 in slides):
    • Meters ↔ Yards: 1 m=1.0936 yd,1 yd=0.9144 m1\text{ m} = 1.0936\text{ yd},\quad 1\text{ yd} = 0.9144\text{ m}
    • Meters ↔ Feet: 1 m=3.2808 ft,1 ft=0.3048 m1\text{ m} = 3.2808\text{ ft},\quad 1\text{ ft} = 0.3048\text{ m}
    • Inches ↔ Meters: 1 in=0.0254 m,1 m=39.37 in1\text{ in} = 0.0254\text{ m},\quad 1\text{ m} = 39.37\text{ in}
    • Kilometers ↔ Miles: 1 km=0.6214 miles,1 mile=1.609 km1\text{ km} = 0.6214\text{ miles},\quad 1\text{ mile} = 1.609\text{ km}
    • Grams ↔ Pounds: 1 g=0.0022 lb,1 lb=454 g1\text{ g} = 0.0022\text{ lb},\quad 1\text{ lb} = 454\text{ g}
    • Kilograms ↔ Pounds: 1 kg=2.20 lb,1 lb=0.454 kg1\text{ kg} = 2.20\text{ lb},\quad 1\text{ lb} = 0.454\text{ kg}
    • Liters ↔ Quarts: 1 L=1.0567 qt,1 qt=0.9464 L1\text{ L} = 1.0567\text{ qt},\quad 1\text{ qt} = 0.9464\text{ L}
    • Liters ↔ Gallons: 1 L=0.2642 gal,1 gal=3.785 L1\text{ L} = 0.2642\text{ gal},\quad 1\text{ gal} = 3.785\text{ L}
  • Quick example conversions (Table 2/3 application):
    • 1 meter ≈ 1.0936 yards
    • 1 yard ≈ 0.9144 meters
    • 1 meter ≈ 3.2808 feet
    • 1 foot ≈ 0.3048 meters
    • 1 inch ≈ 0.0254 meters
    • 1 kilometer ≈ 0.6214 miles
    • 1 mile ≈ 1.609 kilometers
    • 1 gram ≈ 0.0022 pounds
    • 1 pound ≈ 454 grams
    • 1 kilogram ≈ 2.20 pounds
    • 1 pound ≈ 0.454 kilograms
    • 1 liter ≈ 1.0567 quarts
    • 1 quart ≈ 0.9464 liters
    • 1 liter ≈ 0.2642 gallons
    • 1 gallon ≈ 3.785 liters

UNIT CONVERSION PRACTICE (examples)

  • Convert: 12.2 km to mi
    • Using the factor 1 km=0.6214 mi1\text{ km} = 0.6214\text{ mi}
    • Result: 12.2×0.6214≈7.58 mi12.2\times 0.6214 \approx 7.58\ \text{mi}
  • Convert: 1816 g to lb
    • Using 1 g=0.0022 lb1\text{ g} = 0.0022\text{ lb}
    • Result: 1816×0.0022≈3.99 lb≈4.00 lb1816\times 0.0022 \approx 3.99\ \text{lb} \approx 4.00\ \text{lb}
  • Convert: 28.6 L to qt
    • Using 1 L=1.0567 qt1\text{ L} = 1.0567\text{ qt}
    • Result: 28.6×1.0567≈30.22 qt28.6\times 1.0567 \approx 30.22\ \text{qt}
  • Convert: 125 mi to km
    • Using 1 mile=1.609 km1\text{ mile} = 1.609\text{ km}
    • Result: 125×1.609≈201.13 km125\times 1.609 \approx 201.13\ \text{km}
  • Convert: 4 lb to kg
    • Using 1 lb=0.454 kg1\text{ lb} = 0.454\text{ kg}
    • Result: 4×0.454=1.816 kg4\times 0.454 = 1.816\ \text{kg}
  • Convert: 2.5 gal to L
    • Using 1 gal=3.785 L1\text{ gal} = 3.785\text{ L}
    • Result: 2.5×3.785=9.4625 L2.5\times 3.785 = 9.4625\ \text{L}

In-class questions (structure; content not provided in transcript)

  • In-class QUESTION #1
  • In-class QUESTION #2
  • In-class QUESTION #3
  • In-class QUESTION #4
  • In-class QUESTION #5
  • In-class QUESTION #6

Additional notes: Practical implications and connections

  • Understanding unit conversions reduces errors in measurements in science and engineering; it supports accuracy in experiments, data reporting, and cross-disciplinary communication.
  • Real-world relevance includes calculating dosages in nursing, interpreting imaging measurements in radiology, and analyzing laboratory data in biology and chemistry.
  • Ethical/practical considerations:
    • Be mindful of unit accuracy when recording results (e.g., mixing cm with m, or mL with L).
    • Document conversion factors clearly when sharing results to avoid misinterpretation.

Summary of key formulas and facts (quick reference)

  • Length:
    • 1 m=100 cm=1000 mm1\text{ m} = 100\text{ cm} = 1000\text{ mm}
    • 1 cm=0.01 m1\text{ cm} = 0.01\text{ m}
    • 1 km=1000 m1\text{ km} = 1000\text{ m}
  • Volume:
    • 1 cm3=1 mL1\text{ cm}^3 = 1\text{ mL}
    • 1 L=1000 mL1\text{ L} = 1000\text{ mL}
    • 1 mL=1/1000 L1\text{ mL} = 1/1000\text{ L}
  • Mass:
    • 1 kg=1000 g1\text{ kg} = 1000\text{ g}
    • 1 g=1000 mg1\text{ g} = 1000\text{ mg}
  • Temperature:
    • C=59(F−32)C = \dfrac{5}{9}(F - 32)
    • F=95C+32F = \dfrac{9}{5}C + 32
  • Prefixes (power of ten):
    • Giga=109,Mega=106,kilo=103,deci=10−1,centi=10−2,milli=10−3,micro=10−6,nano=10−9\text{Giga}=10^9, \text{Mega}=10^6, \text{kilo}=10^3, \text{deci}=10^{-1}, \text{centi}=10^{-2}, \text{milli}=10^{-3}, \text{micro}=10^{-6}, \text{nano}=10^{-9}
  • Common metric-to-English factors (examples):
    • 1 m=1.0936 yd,  1 yd=0.9144 m1\text{ m} = 1.0936\text{ yd}, \; 1\text{ yd} = 0.9144\text{ m}
    • 1 m=3.2808 ft,  1 ft=0.3048 m1\text{ m} = 3.2808\text{ ft}, \; 1\text{ ft} = 0.3048\text{ m}
    • 1 in=0.0254 m,  1 m=39.37 in1\text{ in} = 0.0254\text{ m}, \; 1\text{ m} = 39.37\text{ in}
    • 1 km=0.6214 miles,  1 mile=1.609 km1\text{ km} = 0.6214\text{ miles}, \; 1\text{ mile} = 1.609\text{ km}
    • 1 g=0.0022 lb,  1 lb=454 g1\text{ g} = 0.0022\text{ lb}, \; 1\text{ lb} = 454\text{ g}
    • 1 kg=2.20 lb,  1 lb=0.454 kg1\text{ kg} = 2.20\text{ lb}, \; 1\text{ lb} = 0.454\text{ kg}
    • 1 L=1.0567 qt,  1 qt=0.9464 L1\text{ L} = 1.0567\text{ qt}, \; 1\text{ qt} = 0.9464\text{ L}
    • 1 L=0.2642 gal,  1 gal=3.785 L1\text{ L} = 0.2642\text{ gal}, \; 1\text{ gal} = 3.785\text{ L}