Metric System in Science and Engineering

• The International System of Units (SI), known as the metric system, is the international standard system of measurement.
• It originated in France in the late 18th century.
• The metric system operates on a base-10 or decimalized system.
• Prefixes differentiate smaller from larger units.

Common Metric System Prefixes

• yotta (Y): 10^24
• zetta (Z): 10^21
• exa (E): 10^18
• peta (P): 10^15
• tera (T): 10^12
• giga (G): 10^9
• mega (M): 10^6
• kilo (k): 10^3
• hecto (h): 10^2
• deka (da): 10^1
• deci (d): 10^-1
• centi (c): 10^-2
• milli (m): 10^-3
• micro (µ): 10^-6
• nano (n): 10^-9
• pico (p): 10^-12
• femto (f): 10^-15
• atto (a): 10^-18
• zepto (z): 10^-21
• yocto (y): 10^-24
• The metric system's base-10 system facilitates easier unit conversion.
• Base units align with defining constants, allowing accurate reproduction anywhere.
• Standard units simplify replication and review of scientific and engineering results.

Metric System Units

• The metric system is standardized and widely used, while the English system is common in the United States.
• Metric system conversion uses factors of 10, while the English system needs conversion ratios.

Base Units

• Base units: serve as the foundation for all other units.
• Each base unit: defined by a standard constant.

Metric System Base Units

• second (s): time
• meter (m): length
• kilogram (kg): mass
• ampere (A): electric current
• kelvin (K): thermodynamic temperature
• mole (mol): amount of substance
• candela (cd): luminous intensity

Derived Units

• Derived units: combinations of base units.
• Area: product of two lengths; unit is m^2.
• Speed: m/s
• Density: kg/m^3
• Volume: m^3

Common Metric Measurements

• Common measurements: length, mass, volume, density, and temperature.

Length

• Length: measure of distance.
• SI unit: meter (m).
• A meter: technically defined by the speed of light in a vacuum at 299,792,458 m/s.
• centi- (10^-2) and milli- (10^-3) are used for small distances.
  • 1 cm = 0.01 m
  • 1 mm = 0.001 m
• kilo- (10^3) and mega- (10^6) are for large distances.
  • 1 km = 1000 m
  • 1 Mm = 1,000,000 m
• Basic units of length in the English system: inch, foot, and mile. Defined in terms of meters.
  • 1 inch (in): exactly 2.54 cm.
  • 1 cm = 0.01 m
• English System Length Conversions:
  • 12 in = 1 ft
  • 3 ft = 1 yd
  • 5280 ft = 1 mi
  • 1760 yd = 1 mi

Mass

• Mass: amount of matter in an object.
• SI unit: kilogram (kg).
• Kilogram definition: tied to the fixed value of the Planck constant at 6.626 070 15 × 10^-34 J s.
• Kilogram: only base unit with a prefix.
  • 1 kilogram = 1000 g.
• Prefixes like milli- (10^-3) and kilo- (10^3): express mass.
• Common units of mass/weight in the English system: ounce (oz), pound (lb), and ton.
  • 1 kg ≈ 2.205 lb.
• English Unit Mass Conversions:
  • 16 oz = 1 lb
  • 2000 lb = 1 ton
• Mass vs. Weight:
  • Mass: amount of matter.
  • Weight: gravitational force on an object.
  • Mass remains constant; weight depends on location.

Volume

• Volume: amount of three-dimensional space occupied.
• Calculated as: length × width × height.
• SI unit: cubic meter (m^3).
• Volume is the space occupied or enclosed by an object.
• A rectangular prism has a volume of V = lwh.
• Prefixes: indicate small/large volumes.
  • 1 m^3 = 1,000,000,000 mm^3 and 1,000,000 cm^3.
• Liter (L): used for liquids, not an official SI unit.
  • 1 liter = 1 cubic decimeter (dm^3) = 1000 cm^3.
• Milliliter (mL): smaller unit.
  • 1000 mL = 1 L.
• Volumes of solids in the English system: cubic feet and cubic yards.
• Common units for fluid volume in the English system: fluid ounce (oz), cup (c), pint (pt), quart (qt), gallon (gal).
• English System Volume Conversions:
  • 1 ft^3 = 1728 in^3
  • 1 yd^3 = 27 ft^3
  • 2 cup = 1 pt
  • 32 oz = 1 qt
  • 2 pt = 1 qt
  • 4 qt = 1 gal

Density

• Density: compactness of an object, determines if it floats or sinks.
• Measured as: mass per unit volume.
• SI unit: kg/m^3.
• Other units: g/mL and g/cm^3.
• Density formula: ρ = m/V, where ρ is density, m is mass, and V is volume.
• To determine if an object floats or sinks, compare its density to water's density (ρ = 1 g/cm^3 or 1000 kg/m^3):
  • Density > water: sink.
  • Density < water: float.

Temperature

• Temperature: hotness or coldness of an object.
• Average kinetic energy of molecules.
• SI unit: kelvin (K).
• Definition: based on the fixed value of the Boltzmann constant, k = 1.380 649 × 10^-23 J/K.
• Three most common temperature scales: Fahrenheit, Celsius, and Kelvin.

Temperature Conversion Formulas

• Celsius to Fahrenheit: °F = (9/5)°C + 32
• Fahrenheit to Celsius: °C = (5/9)(°F - 32)
• Kelvin to Celsius: °C = K - 273.15
• Celsius to Kelvin: K = °C + 273.15
• To convert Fahrenheit to Kelvin, convert to Celsius first.

Metric System Conversion

• Conversion factor: ratio/fraction equal to 1.
• Conversion factor: shows relationship between units.
• The unit to be removed : placed in the denominator
• The desired unit: placed in the numerator.

Converting Large Units to Smaller Units

• To convert 1. 5 km to cm:

  • Use 1 km = 1000 m and 1 m = 100 cm. Convert km to m, then to cm.

• To convert 20 m^3 to mm^3:

  • Use 1 m = 1000 mm. Raise the conversion factors to the power of three.

• To convert 25 tons to g:

  • Use 2000 lb = 1 ton, 1 kg = 2.205 lb, 1 kg = 1000 g.

Converting Smaller Units to Larger Units

• To convert 1500 cm to km:

• To convert 4.25 × 10^7 mm^3 to m^3:

• To convert 1 ton to g:

Explore the widespread use of the metric system in science and engineering. Understand its advantages for precise measurements and simplified conversions. Covers appropriate units and prefixes for various scientific applications.