Metric Units and Conversions

Unit Conversion Overview

• Unit conversion is the process of changing one unit to another.
• Essential units include meters, grams, inches, feet, pounds, and seconds.

Metric Units

• Metric units are universally accepted worldwide, except in the US.
• They are straightforward to convert.
• Base units include meters (m), liters (L), and grams (g); all other metric units derive from these.

Common Metric Prefixes

• Mega: M
• kilo: k
• hecto: h
• deka: da or D
• Base unit: m, l, g
• deci: d
• centi: c
• milli: m
• micro: µ
• nano: n

Metric Conversion Factors

• 1 kilometer (km) = 1000 meters (m)
• 100 centimeters (cm) = 1 meter (m)
• 1000 millimeters (mm) = 1 meter (m)
• Dimensional analysis is used for unit conversion, utilizing equivalence statements between units.

Converting Units of Measurement

• A conversion factor derived from equivalence statements facilitates converting one unit to another.
• Example: To convert centimeters to inches, use the equivalence statement 2.54 cm = 1 in.

Example Conversions

• Converting 3 meters to centimeters:
  • 3 m × (100 cm / 1 m) = 300 cm
• Converting 1516 grams to kilograms:
  • 1516 g × (1 kg / 1000 g) = 1.516 kg
• Converting 7200 mm to kilometers:
  • 7200 mm × (1 cm / 10 mm) × (1 km / 100,000 cm) = 0.0072 km

Non-Metric (English) Unit Conversions

• Common conversion factors:
  • 5280 feet = 1 mile
  • 12 inches = 1 foot
  • 1 mile ≈ 1600 meters
  • 1 inch = 2.54 cm
• Example: To convert 2 miles to feet:
  • 2 mi × (5280 ft / 1 mi) = 10,560 ft

Temperature Conversions

• Three commonly used temperature scales: Fahrenheit, Celsius, and Kelvin.
• To convert Celsius to Kelvin:
  • TK = To + 273
• Example conversion: 70°C = 70 + 273 = 343 K

Converting Between Fahrenheit and Celsius

• To convert Fahrenheit to Celsius:
  • TC = (5/9)(TF - 32)
• Temperature where °C = °F is -40°.

Density

• Density is mass per unit volume, commonly expressed in g/cm³ or g/mL.
• Example: For a mineral with a mass of 17.8 g and a volume of 2.35 cm³,
  • Density = 17.8 g / 2.35 cm³ = 7.57 g/cm³.

Practice Problems

• Convert various measurements using dimensional analysis:
  • 45 inches to cm
  • 8 m to inches
  • 10 ft to cm
  • 5 km to inches
  • 40 km/h to m/s
  • 200 °F to °C
  • 500 K to °C