The US Customary and Metric systems are two major measurement systems used worldwide. Understanding how to convert between units within each system and between the two systems is crucial for practical applications in everyday life and various fields.
Mastering these conversions allows for seamless communication across different measurement standards. From cooking to construction, knowing how to switch between inches and centimeters or and can make a big difference in accurately interpreting and applying measurements.
US Customary System
Conversions within US customary system
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Length
12 inches (in) equal 1 (ft) basic unit of length in
3 feet equal 1 (yd) commonly used for measuring fabric or distances in sports (football field)
5280 feet equal 1 (mi) used for longer distances like travel
Weight
16 ounces (oz) equal 1 (lb) basic unit of weight often used for measuring food ingredients (flour, sugar)
2000 pounds equal 1 (t) used for measuring very heavy objects (vehicles, large quantities of materials)
Volume
8 fluid ounces (fl oz) equal 1 (c) commonly used in cooking and baking recipes
2 cups equal 1 (pt)
2 pints equal 1 (qt) often used for larger liquid volumes (milk)
4 quarts equal 1 (gal) used for even larger volumes like fuel or paint
Calculations with mixed US units
Add or subtract mixed units by converting to the smallest common unit first
Convert each measurement to the smallest unit (inches for length)
Add or subtract the converted values
Convert the result back to mixed units if needed
Example: 2 ft 5 in + 3 ft 8 in
Convert to inches: (2 ft × 12 in/ft + 5 in) + (3 ft × 12 in/ft + 8 in)
Add: 24 in + 5 in + 36 in + 8 in = 73 in
Convert back: 73 in = 6 ft 1 in
Multiply or divide mixed units by converting to a single unit first
Convert the mixed unit measurement to a single unit (feet for length)
Perform the multiplication or division
Convert the result back to mixed units if needed
Example: 2 yd 1 ft × 4
Convert to feet: (2 yd × 3 ft/yd + 1 ft) = 6 ft + 1 ft = 7 ft
Multiply: 7 ft × 4 = 28 ft
Convert back: 28 ft = 9 yd 1 ft
Metric System
Conversions within metric system
Metric prefixes: (k), (h), (da), base unit, (d), (c), (m)
Each prefix represents a power of 10 (kilo = 1000, centi = 1/100)
are the fundamental units of measurement in the (e.g., for length, gram for mass)
Move the decimal point to the right when converting from larger to smaller units
Divide by powers of 10 to go from larger to smaller (km to m, divide by 1000)
Example: 3.5 kilometers (km) = 3500 meters (m)
Move the decimal point to the left when converting from smaller to larger units
Multiply by powers of 10 to go from smaller to larger (mL to L, multiply by 1/1000)
Example: 450 milliliters (mL) = 0.45 liters (L)
Problems with mixed metric units
Convert mixed units to a single unit before performing calculations
Choose the most appropriate unit for the situation (meters for length)
Convert each measurement to the chosen unit
Perform the calculation
Example: 2.3 m + 45 cm
Convert to meters: 2.3 m + 0.45 m
Add: 2.3 m + 0.45 m = 2.75 m
Converting Between Systems
US customary vs metric translations
Length
1 ≈ 2.54 centimeters
1 foot ≈ 0.3048 meters
1 mile ≈ 1.609 kilometers
Volume
1 quart ≈ 0.946 liters
1 gallon ≈ 3.785 liters
Use approximate conversion factors to translate between systems
Multiply US customary unit by conversion factor to get metric equivalent
Divide metric unit by conversion factor to get US customary equivalent
involves changing from one unit of measurement to another while maintaining the same quantity
Fahrenheit vs Celsius conversions
Fahrenheit to Celsius: °C=(°F−32)×95
Subtract 32 from Fahrenheit temperature
Multiply the result by 95
Example: 77°F = (77−32)×95 = 25°C
Celsius to Fahrenheit: °F=°C×59+32
Multiply Celsius temperature by 59
Add 32 to the result
Example: 30°C = 30×59+32 = 86°F
Measurement Precision and Accuracy
refers to the level of detail in a measurement, often indicated by the number of decimal places
is how close a measurement is to the true value
are the meaningful digits in a measurement that contribute to its precision
Key Terms to Review (32)
Accuracy: Accuracy refers to the degree of closeness between a measured or calculated value and the true or accepted value. It is a fundamental concept in various systems of measurement, reflecting the ability to obtain precise and reliable results that closely match the actual quantity being measured.
Base Units: Base units are the fundamental units used to measure different physical quantities in a system of measurement. They serve as the building blocks for more complex units and provide a standardized way to quantify various aspects of the physical world.
Celsius: Celsius is a temperature scale that measures the degree of hotness or coldness of an object or environment. It is widely used in scientific and everyday applications to quantify temperature and is based on the freezing and boiling points of water at standard atmospheric pressure.
Centi-: The prefix 'centi-' is a unit of measurement in the metric system that denotes one-hundredth (1/100) of a base unit. It is commonly used in various contexts related to systems of measurement, particularly in the fields of length, volume, and mass.
Centimeter: A centimeter is a unit of length in the metric system, equal to one-hundredth of a meter. It is a commonly used measurement for small to medium-sized objects and distances in everyday life and scientific applications.
Cup: A cup is a common unit of measurement used to quantify the volume of liquid or dry ingredients in cooking and baking. It is a standardized unit that helps ensure consistent and accurate measurements in recipes.
Deci-: The prefix 'deci-' is a decimal prefix used in the metric system to indicate a factor of one-tenth or 0.1. It is derived from the Latin word 'decem' meaning 'ten.' This prefix is commonly used in various systems of measurement, particularly in the context of the metric system, to represent a fraction or submultiple of a larger unit.
Deka-: The prefix 'deka-' is a metric prefix that denotes a factor of 10. It is used to indicate a multiple of 10 in the International System of Units (SI). The prefix 'deka-' is commonly used in the context of systems of measurement to represent larger units of measurement.
Fahrenheit: Fahrenheit is a temperature scale that measures the degree of heat or cold. It is commonly used in the United States and a few other countries, and it is based on the freezing and boiling points of water under standard atmospheric pressure.
Fluid Ounce: A fluid ounce is a unit of volume measurement commonly used in the United States to measure the volume of liquid substances. It is a part of the customary system of measurement and is often used to measure the volume of beverages, medicines, and other liquids.
Foot: A foot is a unit of length in the Imperial and United States customary systems of measurement, equal to 12 inches or one-third of a yard. It is a fundamental unit used to measure distance, height, and other physical quantities.
Gallon: A gallon is a unit of volume measurement, primarily used in the United States and some other countries, to quantify the capacity of containers and the volume of liquids and gases. It is a widely recognized and commonly used unit in various systems of measurement, particularly in the context of systems of measurement.
Hecto-: The prefix 'hecto-' is a unit prefix in the metric system that represents a factor of one hundred. It is derived from the Greek word 'hekaton' meaning one hundred. This prefix is used to denote multiples of a base unit, indicating a quantity that is one hundred times larger than the original unit.
Inch: The inch is a unit of length in various systems of measurement, commonly used to measure small distances or the dimensions of objects. It is a fundamental unit in the Imperial and United States Customary systems of measurement, with historical origins dating back to ancient civilizations.
Kilo-: The prefix 'kilo-' is a metric system prefix that represents a factor of 1,000. It is commonly used to denote multiples of units of measurement, particularly in the context of systems of measurement.
Kilometer: A kilometer is a unit of length in the metric system, equal to one thousand meters. It is commonly used to measure long distances, such as the length of roads, the distance between cities, or the circumference of the Earth.
Liter: A liter is a unit of volume in the metric system, primarily used to measure the capacity of containers. It is a fundamental unit in the context of systems of measurement and solving mixture applications.
Meter: A meter is the base unit of length in the International System of Units (SI), used to measure and quantify physical distance or dimensions. It is a fundamental unit that serves as the foundation for various systems of measurement, including the metric system.
Metric System: The metric system is a decimal-based system of measurement that uses standard units for length, mass, volume, and other quantities. It is the predominant system of measurement used worldwide and is based on the fundamental units of the meter, gram, and liter.
Mile: A mile is a unit of length in the Imperial and United States customary systems of measurement. It is defined as the distance traveled by 5,280 feet or 1,760 yards. The mile is commonly used to measure long distances, particularly for land travel and navigation.
Milli-: The prefix 'milli-' is a unit of measurement that represents one-thousandth (1/1,000) of a base unit. It is commonly used in the metric system to denote small quantities or measurements.
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.
Ounce: An ounce is a unit of measurement used to quantify the mass or weight of an object. It is a commonly used unit in the imperial system of measurement, particularly in the United States, for measuring the weight of various substances, including food, liquids, and other materials.
Pint: A pint is a unit of volume used in the imperial and US customary systems of measurement. It is a commonly used unit for measuring the volume of liquids and certain dry goods.
Pound: The pound is a unit of mass and weight in various systems of measurement, primarily used in the United States and other countries that have historically been influenced by the British imperial system. It is a fundamental unit that serves as a reference point for quantifying and comparing the mass or weight of physical objects.
Precision: Precision refers to the degree of exactness or the fineness of measurement. It is a measure of how close a series of measurements are to one another, without regard to how close they are to the true value.
Quart: A quart is a unit of volume measurement in the customary system of measurement, commonly used to measure the capacity of containers for liquids and dry goods. It is a standard unit of volume in the United States and is equivalent to one-fourth of a gallon.
Significant Figures: Significant figures refer to the meaningful digits in a numerical value, including both the certain digits and the estimated or uncertain digits. This concept is essential in the context of decimal operations, systems of measurement, and scientific notation, as it helps determine the precision and reliability of numerical data.
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 metric system and the imperial system, and is commonly used in industries such as transportation, manufacturing, and agriculture.
Unit Conversion: Unit conversion is the process of changing a measurement from one unit to another equivalent unit, allowing for consistent and meaningful comparisons across different systems of measurement. This concept is essential in various mathematical applications, including solving problems related to systems of measurement, mixture applications, and uniform motion.
US Customary System: The US Customary System is a system of measurement units that is widely used in the United States. It is the primary system of measurement for everyday purposes, such as in the measurement of length, weight, volume, and temperature, and is the basis for many of the units commonly used in the country.
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 fingertips of an average-sized man, which is approximately 36 inches or 0.9144 meters. The yard is a fundamental unit in systems of measurement that are widely used for various applications, including construction, transportation, and everyday activities.