Skip to main content
Mathematics LibreTexts

1.5: Chapter Review and Glossary

  1. Last updated
  2. Save as PDF
  • Page ID
    113122

    • \( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \) \( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}} \)\(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\) \(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\)\(\newcommand{\AA}{\unicode[.8,0]{x212B}}\)

    Chapter Review

    1.1: Length

    The four basic units of measurement that are used for length in the U.S. customary measurement system are: inch, foot, yard, and mile. Typically, people use yards, miles, and sometimes feet to describe long distances. Measurement in inches is common for shorter objects or lengths. You need to convert from one unit of measure to another if you are solving problems that include measurements involving more than one type of measurement. Each of the units can be converted to one of the other units using the table of equivalents, the conversion factors, and/or the factor label method shown in this topic.

    1.1: Weight

    In the U.S. customary system of measurement, weight is measured in three units: ounces, pounds, and tons. A pound is equivalent to 16 ounces, and a ton is equivalent to 2,000 pounds. While an object’s weight can be described using any of these units, it is typical to describe very heavy objects using tons and very light objects using an ounce. Pounds are used to describe the weight of many objects and people. Often, in order to compare the weights of two objects or people or to solve problems involving weight, you must convert from one unit of measurement to another unit of measurement. Using conversion factors with the factor label method is an effective strategy for converting units and solving problems.

    1.1: Capacity

    There are five basic units for measuring capacity in the U.S. customary measurement system. These are the fluid ounce, cup, pint, quart, and gallon. These measurement units are related to one another, and capacity can be described using any of the units. Typically, people use gallons to describe larger quantities and fluid ounces, cups, pints, or quarts to describe smaller quantities. Often, in order to compare or to solve problems involving the amount of liquid in a container, you need to convert from one unit of measurement to another.

    1.2: The Metric System

    The metric system is an alternative system of measurement used in most countries, as well as in the United States. The metric system is based on joining one of a series of prefixes, including kilo- , hecto-, deka-, deci-, centi-, and milli-, with a base unit of measurement, such as meter, liter, or gram. Units in the metric system are all related by a power of 10, which means that each successive unit is 10 times larger than the previous one. This makes converting one metric measurement to another a straightforward process, and is often as simple as moving a decimal point. It is always important, though, to consider the direction of the conversion. If you are converting a smaller unit to a larger unit, then the decimal point has to move to the left (making your number smaller); if you are converting a larger unit to a smaller unit, then the decimal point has to move to the right (making your number larger).

    1.2: Converting within the Metric System

    To convert among units in the metric system, identify the unit that you have, the unit that you want to convert to, and then count the number of units to move between them. If you are going from a larger unit to a smaller unit, you multiply by 10 successively. If you are going from a smaller unit to a larger unit, you divide by 10 successively. You can also move the decimal point of your number the same direction and same number of spots that you need to move from the original unit to the new unit. The factor label method can also be applied to conversions within the metric system. To use the factor label method, you multiply the original measurement by unit fractions; this allows you to represent the original measurement in a different measurement unit.

    1.2: Using Metric Conversion to Solve Problems

    Understanding the context of real-life application problems is important. Look for words within the problem that help you identify what operations are needed, and then apply the correct unit conversions. Checking your final answer by using another conversion method (such as the “move the decimal” method, if you have used the factor label method to solve the problem) can cut down on errors in your calculations.

    1.3: Temperature and time

    Temperature is often measured in one of two scales: the Celsius scale and the Fahrenheit scale. A Celsius thermometer will measure the boiling point of water at 100° and its freezing point at 0°; a Fahrenheit thermometer will measure the same events at 212° for the boiling point of water and 32° as its freezing point. You can use conversion formulas to convert a measurement made in one scale to the other scale. Time is universal and is measured in seconds, minutes, hours, days, weeks and years.

    1.4: Conversion Between the Metric and US Customary Systems of Measurement

    To convert metric units to US customary units or vice versa, use their estimate equivalence as the conversion factor in dimensional analysis. Write the equivalence as a fraction, and multiply it to the given measurement to convert. Be sure that the units of measure to convert cancels out.

    Glossary:

    capacity The amount of liquid (or other pourable substance) that an object can hold when it's full.
    Celsius A measure of temperature commonly used in countries that use the metric system. On the Celsius scale, water freezes at 0° and boils at 100°.
    cup A unit of capacity equal to 8 fluid ounces.
    factor label method One method of converting a measurement from one unit of measurement to another unit of measurement. In this method, you multiply the original measurement by unit fractions containing different units of measurement to obtain the new unit of measurement.
    Fahrenheit A measure of temperature commonly used in the United States. On the Fahrenheit scale, water freezes at 32° F and boils at 212° F.
    fluid ounce A unit of capacity equal to \(\dfrac{1}{8}\) of a cup. One fluid ounce of water at 62°F weighs about one ounce.
    foot A unit for measuring length in the U.S. customary measurement system. 1 foot = 12 inches
    gallon A unit equal to 4 quarts, or 128 fluid ounces.
    gram The base unit of mass in the metric system.
    inch A unit for measuring length in the U.S. customary measurement system. 1 foot = 12 inches
    length The distance from one end to the other or the distance from one point to another.
    liter The base unit of capacity in the metric system.
    measurement The use of standard units to find out the size or quantity of items such as length, width, height, mass, weight, volume, temperature or time.
    meter The base unit of length in the metric system.
    metric system A widely-used system of measurement that is based on the decimal system and multiples of 10.
    mile A unit for measuring length in the U.S. customary measurement system. 1 mile = 5280 feet or 1760 yards.
    ounce A unit for measuring weight in the U.S. customary measurement system. 16 ounces = 1 pound.
    pint A unit of capacity equal to 16 fluid ounces, or 2 cups.
    pound A unit for measuring weight in the U.S. customary measurement system. 16 ounces = 1 pound.
    prefix A short set of letters that denote the size of measurement units in the metric system. Metric prefixes include kilo-, hecto-, deka-, deci-, centi-, and milli-
    quart A unit of capacity equal to 32 fluid ounces, or 4 cups.
    ton A unit for measuring the weight of heavier items in the U.S. customary measurement system. 1 ton = 2000 pounds.
    U.S. customary measurement system The most common system of measurement used in the United States. It is based on English measurement systems of the 18th century.
    unit equivalents Statements of equivalence between measurement units within a system or in comparison to another system of units. For example, 1 foot = 12 inches or 1 inch = 2.54 centimeters are both examples of unit equivalents.
    unit fractions A fraction where the numerator and denominator are equal amounts, as in \(\dfrac{1 \text{ kg}}{1000 \text{ g}}\) or \(\dfrac{12 \text{ inches}}{1 \text{ foot}}\). Unit fractions serve to help with conversions in the factor label method (dimensional analysis).
    unit of measurement A standard amount or quantity. For example, an inch is a unit of measurement.
    weight A mathematical description of how heavy an object is.
    yard A unit for measuring length in the U.S. customary measurement system. 1 yard = 3 feet or 36 inches.

    This page titled 1.5: Chapter Review and Glossary is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by Darlene Diaz (ASCCC Open Educational Resources Initiative) via source content that was edited to the style and standards of the LibreTexts platform; a detailed edit history is available upon request.