Metric System Overview

Overview

This lecture explains metric system base units, common metric prefixes, and step-by-step methods for converting between metric and non-metric units with examples.

Metric System Base Units

• The metric system is based on units of 10 for easy conversion.
• Base units: liters (L) for volume, meters (m) for length, grams (g) for mass/weight.
• Metric prefixes mean the same regardless of the base unit used.

Common Metric Prefixes

• Kilo- (k): 1000 times the base unit (e.g., 1 kilometer = 1000 meters).
• Centi- (c): 1/100 of the base unit (e.g., 1 centimeter = 0.01 meters, or 100 centimeters = 1 meter).
• Milli- (m): 1/1000 of the base unit (e.g., 1 milligram = 0.001 grams, or 1000 milligrams = 1 gram).
• Micro- (µ): 1/1,000,000 of the base unit (e.g., 1 microliter = 0.000001 liters, or 1,000,000 microliters = 1 liter).

Metric Conversion Method

• Always start with what is given and write down the relevant equivalency (conversion factor).
• Set up a fraction so that the unit you want to cancel is opposite (numerator/denominator) your starting unit.
• Multiply across the top and divide by the bottom to get your answer in the new unit.
• Always include units in your setup and final answer.

Single-Step Conversion Examples

• Convert 22 grams to milligrams: 22 g × (1000 mg / 1 g) = 22,000 mg.
• Convert 7.4 kilometers to meters: 7.4 km × (1000 m / 1 km) = 7,400 m.

Multi-Step Conversion Examples

• To convert 2000 milliliters to quarts (using 1 quart = 0.95 liters):
  • 2000 mL × (1 L / 1000 mL) × (1 qt / 0.95 L) = 2.1 quarts.
• To convert 12 meters to inches (using 1 in = 2.54 cm):
  • 12 m × (100 cm / 1 m) × (1 in / 2.54 cm) = 472.44 inches.

Tips for Metric Conversions

• Recognize when multiple steps are needed (if the conversion factor does not use your starting unit).
• Write down all steps and conversion fractions.
• Practice to recognize patterns and become comfortable with conversions.

Key Terms & Definitions

• Base unit — Basic measurement unit (meter, liter, gram) in the metric system.
• Prefix — Modifier indicating the power of ten (e.g., kilo-, centi-, milli-, micro-).
• Conversion factor — Ratio expressing how many of one unit equals another unit.
• Equivalent numbers — Numbers showing the relationship between two units (e.g., 1000 mg = 1 g).

Action Items / Next Steps

• Practice additional metric conversion problems.
• Attend office hours for extra help if needed.
• Check answers with posted answer key only after attempting problems on your own.