💯Math for Non-Math Majors Unit 9 – Metric System Basics

What's the Deal with the Metric System?

• Standardized system of measurement used globally in science, medicine, and most countries
• Based on powers of 10, making conversions between units straightforward
• Consists of base units for fundamental quantities (meter, gram, liter)
• Prefixes added to base units indicate larger or smaller quantities (kilometer, centimeter)
• Developed during the French Revolution to replace inconsistent regional measurement systems
  • Aimed to create a rational, universal system accessible to all
• Officially adopted in France in 1795 and spread worldwide in the 19th and 20th centuries
• Preferred in scientific and technical fields for its simplicity and consistency

Key Units and Their Abbreviations

• Meter (m): base unit of length, originally defined as one ten-millionth of the distance from the equator to the North Pole
• Gram (g): base unit of mass, originally defined as the mass of one cubic centimeter of water at its maximum density
• Liter (L): base unit of volume, equal to the volume of a cube with 10 cm sides
• Second (s): base unit of time, defined by the oscillations of a cesium-133 atom
• Ampere (A): base unit of electric current, defined by the flow of elementary charges per second
• Kelvin (K): base unit of temperature, defined by the triple point of water (273.16 K)
• Mole (mol): base unit of amount of substance, equal to the number of atoms in 12 grams of carbon-12

Converting Between Metric Units

• Metric system uses prefixes to indicate multiples or fractions of base units
  • For example, kilo- means 1,000 times the base unit, so 1 kilometer = 1,000 meters
• To convert between units, move the decimal point based on the prefix
  • Moving the decimal point to the right makes the number smaller (dividing)
  • Moving the decimal point to the left makes the number larger (multiplying)
• Example: converting 5,000 milliliters to liters
  • Milli- means one-thousandth, so move the decimal point three places to the left
  • 5,000 mL = 5 L
• Converting between units with different prefixes
  • Determine the number of "steps" between prefixes and move the decimal accordingly
  • Example: converting 0.05 kilometers to centimeters
    • Kilo- to centi- is 5 steps (kilo, hecto, deca, base, deci, centi), so move the decimal 5 places to the right
    • 0.05 km = 5,000 cm

Metric Prefixes: Kilo, Centi, Milli, and More

• Prefixes added to base units to indicate larger or smaller quantities
• Most commonly used prefixes:
  • Kilo- (k): 1,000 times the base unit
  • Hecto- (h): 100 times the base unit
  • Deca- (da): 10 times the base unit
  • Deci- (d): one-tenth of the base unit
  • Centi- (c): one-hundredth of the base unit
  • Milli- (m): one-thousandth of the base unit
• Less common prefixes:
  • Mega- (M): 1,000,000 times the base unit
  • Micro- (μ): one-millionth of the base unit
  • Nano- (n): one-billionth of the base unit
• Prefixes can be combined with any base unit
  • Examples: kilometer (km), centimeter (cm), milligram (mg), milliliter (mL)

Comparing Metric to US Customary Units

• US Customary system used in the United States, based on English units
• Key differences between Metric and US Customary:
  • Metric uses powers of 10 for conversions, US Customary has inconsistent conversion factors
  • Metric units are related to each other, US Customary units are independent
• Common US Customary units and their Metric equivalents:
  • Length: 1 inch ≈ 2.54 centimeters, 1 foot ≈ 0.3048 meters, 1 mile ≈ 1.609 kilometers
  • Mass: 1 ounce ≈ 28.35 grams, 1 pound ≈ 0.454 kilograms
  • Volume: 1 fluid ounce ≈ 29.57 milliliters, 1 quart ≈ 0.946 liters, 1 gallon ≈ 3.785 liters
• Rough conversions for everyday use:
  • 1 inch ≈ 2.5 centimeters
  • 1 foot ≈ 30 centimeters
  • 1 pound ≈ 0.5 kilograms
  • 1 quart ≈ 1 liter

Real-World Applications of the Metric System

• Scientific research and calculations
  • Consistent, easily convertible units essential for accurate measurements and data sharing
• Medicine and healthcare
  • Dosages of medications, fluid volumes, and patient measurements in metric units
• Engineering and manufacturing
  • Metric system enables standardization and compatibility of parts across industries and countries
• International trade
  • Metric system facilitates communication and reduces confusion between trading partners
• Cooking and baking
  • Metric recipes use weight measurements (grams) for dry ingredients, ensuring consistency
• Athletics and sports
  • Track and field events, swimming pools, and ski jumps measured in metric units worldwide

Common Metric System Pitfalls and How to Avoid Them

• Confusing prefixes or incorrectly converting between units
  • Double-check the prefix and the number of decimal places moved
• Mixing up Celsius and Fahrenheit temperatures
  • Celsius: water freezes at 0°C and boils at 100°C
  • Fahrenheit: water freezes at 32°F and boils at 212°F
• Incorrectly reading metric rulers or measuring tools
  • Ensure you're counting the correct number of tick marks for centimeters and millimeters
• Rounding errors when converting between Metric and US Customary
  • Use precise conversion factors and be aware of the required level of accuracy
• Forgetting to include units when recording measurements
  • Always specify the unit to avoid ambiguity and errors in calculations

Practice Problems and Quick Tips

• Convert 3.5 kilometers to meters
  • Move the decimal point 3 places to the right (kilo to base)
  • 3.5 km = 3,500 m
• Convert 450 centimeters to meters
  • Move the decimal point 2 places to the left (centi to base)
  • 450 cm = 4.5 m
• Convert 2,000 grams to kilograms
  • Move the decimal point 3 places to the left (base to kilo)
  • 2,000 g = 2 kg
• Quick tip: use mnemonic devices to remember prefixes and their meanings
  • "King Henry Died Unexpectedly Drinking Chocolate Milk" (Kilo, Hecto, Deca, base, deci, centi, milli)
• Quick tip: practice mental conversions between common Metric and US Customary units
  • 1 inch ≈ 2.5 cm, 1 foot ≈ 30 cm, 1 pound ≈ 0.5 kg, 1 quart ≈ 1 liter