The U.S. Customary and Metric systems are two different ways to measure things. They use different units and conversion rules. Understanding how to switch between them is key for solving real-world math problems.

Converting units within each system and between them is a crucial skill. It helps in everyday tasks like cooking, shopping, and traveling. Knowing these conversions allows you to work with measurements from different parts of the world.

U.S. Customary System

Conversions within U.S. customary system

• Length measurements interrelated by specific ratios (1 foot = 12 inches, 1 yard = 3 feet, 1 mile = 5,280 feet)
• Weight measurements connected through conversion factors (1 pound = 16 ounces, 1 ton = 2,000 pounds)
• Volume units linked by proportional relationships (1 cup = 8 fluid ounces, 1 pint = 2 cups, 1 quart = 2 pints, 1 gallon = 4 quarts)

Calculations with mixed U.S. units

• Adding or subtracting requires same unit type (5 inches + 3 inches = 8 inches, 2 pounds - 0.5 pounds = 1.5 pounds)
• Multiplying or dividing allows different unit types (2 feet × 3 pounds = 6 foot-pounds, 1 gallon ÷ 2 minutes = 0.5 gallons per minute)
• Converting units necessary before calculation if units mismatch (3 feet + 6 inches requires converting 6 inches to 0.5 feet first)

Metric System

Conversions within metric system

• Metric prefixes indicate powers of 10 relative to base unit (kilo = 1000, hecto = 100, deka = 10, deci = 0.1, centi = 0.01, milli = 0.001)
• Converting involves shifting decimal point based on prefix change (3.5 kilometers = 3500 meters, 275 centimeters = 2.75 meters)
• Metric system designed for easy conversions by factors of 10
• Base units (such as meter, gram, or liter) serve as the foundation for all other units in the system

Problems with mixed metric units

• Identify base unit for given quantity (meters for length, grams for mass, liters for volume)
• Convert mixed units to common prefix before calculating (2 kilometers + 500 meters requires converting to 2500 meters + 500 meters)
• Perform calculation and express result in desired metric unit (2500 m + 500 m = 3000 m or 3 km)

Converting Between Systems

U.S. customary vs metric translations

• Conversion factors bridge U.S. customary and metric systems (1 inch ≈ 2.54 centimeters, 1 pound ≈ 0.454 kilograms, 1 quart ≈ 0.946 liters)
• Multiply given measurement by appropriate conversion factor to translate (5 inches × 2.54 cm/in = 12.7 cm, 2 pounds × 0.454 kg/lb ≈ 0.908 kg)
• Reverse conversion divides by factor instead of multiplying (12.7 cm ÷ 2.54 cm/in = 5 inches)

Fahrenheit vs Celsius conversions

• Fahrenheit to Celsius formula $°C = (°F - 32) × \frac{5}{9}$ (77°F plugged in yields 25°C)
• Celsius to Fahrenheit formula $°F = (°C × \frac{9}{5}) + 32$ (25°C plugged in yields 77°F)
• Key reference points help estimate conversions (water freezes at 32°F or 0°C, boils at 212°F or 100°C)

International System of Units (SI)

• The International System of Units (SI) is the modern form of the metric system
• SI uses standardized base units for fundamental quantities
• Prefixes are used to create multiples and submultiples of base units
• Conversion factors are essential for translating between SI and other measurement systems