7.5 Systems of Measurement
3 min read•june 25, 2024
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
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- Length measurements interrelated by specific ratios (1 = 12 inches, 1 = 3 feet, 1 = 5,280 feet)
- Weight measurements connected through conversion factors (1 = 16 ounces, 1 = 2,000 pounds)
- Volume units linked by proportional relationships (1 = 8 fluid ounces, 1 = 2 cups, 1 = 2 pints, 1 = 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 (kilo = 1000, hecto = 100, deka = 10, deci = 0.1, centi = 0.01, milli = 0.001)
- Converting involves shifting decimal point based on change (3.5 kilometers = 3500 meters, 275 centimeters = 2.75 meters)
- designed for easy conversions by factors of 10
- Base units (such as , , or ) 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 ≈ 2.54 centimeters, 1 pound ≈ 0.454 kilograms, 1 quart ≈ 0.946 liters)
- Multiply given measurement by appropriate 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
- to formula (77°F plugged in yields 25°C)
- Celsius to Fahrenheit formula (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 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
Key Terms to Review (35)
Base Unit: A base unit is the fundamental unit of measurement within a system of measurement, serving as the foundation for deriving other units. It is the starting point from which all other units are defined and calculated.
Celsius: Celsius is a temperature scale that is widely used around the world to measure temperature. It is based on the freezing and boiling points of water, with 0 degrees Celsius representing the freezing point and 100 degrees Celsius representing the boiling point of water at standard atmospheric pressure.
Centi-: The prefix 'centi-' is a metric system prefix that represents one-hundredth (1/100) of a unit. It is derived from the Latin word 'centum,' meaning one hundred. The prefix 'centi-' is commonly used in the context of systems of measurement, particularly in the International System of Units (SI), to denote smaller units of measurement.
Centimeter: A centimeter (cm) is a unit of length in the metric system, equal to one-hundredth of a meter. It is commonly used to measure small distances and the dimensions of objects.
Conversion Factor: A conversion factor is a numerical value used to convert one unit of measurement to another equivalent unit within the same system or between different measurement systems. It allows for the seamless translation of quantities expressed in one set of units to their corresponding values in another set of units.
Cup: A cup is a unit of volume measurement commonly used in cooking and baking recipes. It is a standard unit that helps ensure consistent measurements and proportions when preparing food and beverages.
Deci-: The prefix 'deci-' is a unit prefix in the metric system that denotes a factor of one-tenth or 0.1. It is used to indicate a decimal submultiple of a unit, allowing for the standardization and organization of measurements across various systems.
Deka-: The prefix 'deka-' is a metric prefix that denotes a factor of 10. It is used to represent multiples of 10 in the International System of Units (SI) and other systems of measurement. The prefix 'deka-' is particularly relevant in the context of systems of measurement, as it helps to define and quantify various units of measurement.
Fahrenheit: Fahrenheit is a temperature scale that measures the degree of heat or cold. It was developed by the German physicist Daniel Gabriel Fahrenheit in the early 18th century and is commonly used in the United States and a few other countries. The Fahrenheit scale is based on the freezing and boiling points of water, with the freezing point set at 32 degrees and the boiling point at 212 degrees.
Fluid Ounce: A fluid ounce is a unit of volume used to measure the capacity of liquids. It is a commonly used unit in the United States customary system of measurement and is often abbreviated as fl oz or fl. oz.
Foot: The foot is a complex anatomical structure that serves as the foundation for the human body, providing support, balance, and mobility. It is the lowermost part of the leg, consisting of multiple bones, joints, and soft tissues that work together to facilitate various movements and functions.
Gallon: A gallon is a unit of measurement for volume, commonly used to measure the capacity of containers, particularly for liquids. It is a standard unit of measurement in the United States customary system and is widely used in various applications, including the measurement of fuel, water, and other fluids.
Gram: A gram is a unit of measurement in the metric system that is used to measure the mass or weight of an object. It is a fundamental unit in the International System of Units (SI) and is widely used in various scientific and everyday applications.
Hecto-: The prefix 'hecto-' is a unit prefix in the metric system that denotes a factor of one hundred. It is derived from the Greek word 'hekaton' meaning one hundred. This prefix is used to represent multiples of a base unit, allowing for efficient and standardized measurement across various systems.
Inch: An inch is a unit of length in the imperial and United States customary measurement systems. It is commonly used to measure small distances and the dimensions of various objects.
International System of Units (SI): The International System of Units (SI) is the modern standardized metric system of measurement used worldwide. It provides a coherent and universally accepted framework for quantifying various physical quantities, enabling consistent and precise measurements across different scientific and technological fields.
Kilo-: The prefix 'kilo-' is a metric system prefix that denotes a factor of one thousand. It is commonly used in the context of measurement systems to indicate a multiple of the base unit by a factor of 1,000. This prefix is particularly relevant when discussing systems of measurement, as it allows for the expression of larger quantities in a concise and standardized manner.
Kilogram: The kilogram is the base unit of mass in the International System of Units (SI). It is defined as the mass of the international prototype of the kilogram, a platinum-iridium cylinder kept at the International Bureau of Weights and Measures in Sèvres, France. The kilogram is a fundamental unit used to measure the amount of matter in an object and is essential for understanding systems of measurement.
Kilometer: A kilometer is a unit of length in the metric system, equal to 1,000 meters or approximately 0.62 miles. It is a commonly used measure for expressing distances, particularly in the context of transportation and geography.
Liter: A liter is a unit of volume measurement in the metric system, primarily used to measure the capacity of containers and the volume of liquids and gases. It is a fundamental unit in the International System of Units (SI) and is widely used in various scientific and everyday applications.
Meter: A meter is the fundamental unit of length in the International System of Units (SI). It is the base unit used to measure distance, height, width, and other linear dimensions. The meter serves as the foundation for the measurement of various physical quantities within the metric system.
Metric System: The metric system is a decimal-based system of measurement that is widely used globally. It provides a standardized and logical framework for measuring various quantities, including length, mass, volume, and temperature, using a consistent set of units and prefixes.
Mile: A mile is a unit of length in the imperial and United States customary systems of measurement, equal to 5,280 feet or 1,609 meters. It is commonly used to measure distances, particularly for long-distance travel and navigation.
Milli-: The prefix 'milli-' is a unit prefix in the metric system that denotes one-thousandth (1/1000) of a base unit. It is commonly used to represent small measurements in various systems of measurement, particularly in the context of length, mass, and volume.
Milligram: A milligram (mg) is a unit of measurement used to quantify very small masses or amounts, particularly in the context of medicine, nutrition, and scientific research. It is a metric unit that represents one-thousandth of a gram, making it a crucial tool for precisely measuring and administering substances in small quantities.
Milliliter: A milliliter (mL) is a unit of volume in the metric system, representing one-thousandth of a liter. It is commonly used to measure small volumes of liquids and is an important unit in the context of systems of measurement.
Millimeter: A millimeter (mm) is a unit of length in the metric system, representing one-thousandth of a meter. It is commonly used to measure small distances and dimensions, particularly in the fields of engineering, science, and everyday life.
Ounce: An ounce is a unit of measurement for weight or mass, commonly used in the United States and other countries that utilize the imperial system. It is a small unit of measurement that is often used to quantify the weight of various items, from food and beverages to precious metals and other materials.
Pint: A pint is a unit of volume used to measure liquid and dry ingredients in the imperial and US customary systems of measurement. It is a commonly used unit in everyday cooking and beverage consumption.
Pound: The pound is a unit of mass and weight in various systems of measurement, commonly used to quantify the weight or mass of an object. It is a fundamental unit in the Imperial and United States Customary systems of measurement, with historical origins tracing back to ancient Roman and English units of measurement.
Prefix: A prefix is a letter or group of letters that is added to the beginning of a word to modify its meaning or create a new word. Prefixes are commonly used in the context of systems of measurement to denote specific units or quantities.
Quart: A quart is a unit of volume measurement in the United States customary system and the imperial system. It is commonly used to measure the capacity of containers for liquids and dry goods.
Ton: A ton is a unit of measurement used to quantify mass or weight, typically in the context of large or heavy objects. It is a standard unit of measurement in various systems, including the imperial and metric systems, and is commonly used in industries such as transportation, construction, and manufacturing.
U.S. Customary System: The U.S. Customary System is the primary system of measurement used in the United States. It is a system of units that includes measurements for length, weight, volume, and other physical quantities, and is distinct from the International System of Units (SI) or metric system used in most other countries.
Yard: A yard is a unit of length in the imperial and United States customary systems of measurement. It is defined as the distance between the tip of the nose and the outstretched thumb of the average-sized man, which is approximately 36 inches or 0.9144 meters. Yards are commonly used to measure distance, height, and length in various applications, from construction to sports.