{"id":91,"date":"2017-12-14T21:25:43","date_gmt":"2017-12-14T21:25:43","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/suny-mcc-introductorychemistry\/chapter\/expressing-units\/"},"modified":"2022-12-08T20:06:42","modified_gmt":"2022-12-08T20:06:42","slug":"expressing-units","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/suny-mcc-introductorychemistry\/chapter\/expressing-units\/","title":{"raw":"2.2 Expressing Units","rendered":"2.2 Expressing Units"},"content":{"raw":"
\r\n
\r\n
\r\n

Learning Objectives<\/h3>\r\n
    \r\n \t
  1. Learn the units that go with various quantities.<\/li>\r\n \t
  2. Express units using their abbreviations.<\/li>\r\n \t
  3. Make new units by combining numerical prefixes with units.<\/li>\r\n<\/ol>\r\n<\/div>\r\n<\/div>\r\n

    A number indicates \u201chow much,\u201d but the unit indicates \u201cof what.\u201d The \u201cof what\u201d is important when communicating a quantity. For example, if you were to ask a friend how close you are to Lake Erie and your friend says \u201csix,\u201d then your friend isn\u2019t giving you complete information. Six what<\/em>? Six miles? Six inches? Six city blocks? The actual distance to the lake depends on what units you use.<\/p>\r\nThe number in the measurement can be represented in different ways, including decimal form and scientific notation. For example, the maximum takeoff weight of a Boeing 777 airliner is 298,000 kilograms, which can also be written as 2.98 \u00d7 105<\/sup> kg. The mass of the average mosquito is about 0.0000025 kilograms, which can be written as 2.5 \u00d7 10\u22126<\/sup> kg.\r\n\r\nUnits<\/strong>, such as liters, pounds, and centimeters, are standards of comparison for measurements. When we buy a 2-liter bottle of a soft drink, we expect that the volume of the drink was measured, so it is two times larger than the volume that everyone agrees to be 1 liter. The meat used to prepare a 0.25-pound hamburger is measured so it weighs one-fourth as much as 1 pound. Without units, a number can be meaningless, confusing, or possibly life threatening. Suppose a doctor prescribes phenobarbital to control a patient\u2019s seizures and states a dosage of \u201c100\u201d without specifying units. Not only will this be confusing to the medical professional giving the dose, but the consequences can be dire: 100 mg given three times per day can be effective as an anticonvulsant, but a single dose of 100 g is more than 10 times the lethal amount.\r\n\r\nWe usually report the results of scientific measurements in SI units, an updated version of the metric system, using the units listed in Table\u00a01. Other units can be derived from these base units. The standards for these units are fixed by international agreement, and they are called the International System of Units<\/strong> or SI Units <\/strong>(from the French, Le Syst\u00e8me International d\u2019Unit\u00e9s<\/em>). SI units have been used by the United States National Institute of Standards and Technology (NIST) since 1964.\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n
    Table\u00a01. Base Units of the SI System<\/th>\r\n<\/tr>\r\n
    Property Measured<\/th>\r\nName of Unit<\/th>\r\nSymbol of Unit<\/th>\r\n<\/tr>\r\n<\/thead>\r\n
    length<\/td>\r\nmeter<\/td>\r\nm<\/td>\r\n<\/tr>\r\n
    mass<\/td>\r\nkilogram<\/td>\r\nkg<\/td>\r\n<\/tr>\r\n
    time<\/td>\r\nsecond<\/td>\r\ns<\/td>\r\n<\/tr>\r\n
    temperature<\/td>\r\nkelvin<\/td>\r\nK<\/td>\r\n<\/tr>\r\n
    amount of substance<\/td>\r\nmole<\/td>\r\nmol<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\nSometimes we use units that are fractions or multiples of a base unit. Ice cream is sold in quarts (a familiar, non-SI base unit), pints (0.5 quart), or gallons (4 quarts). We also use fractions or multiples of units in the SI system, but these fractions or multiples are always powers of 10. Fractional or multiple SI units are named using a prefix and the name of the base unit. For example, a length of 1000 meters is also called a kilometer because the prefix kilo<\/em> means \u201cone thousand,\u201d which in scientific notation is 103<\/sup> (1 kilometer = 1000 m = 103<\/sup> m). The prefixes used and the powers to which 10 are raised are listed in Table\u00a02.\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n
    Table\u00a02. Common Unit Prefixes<\/th>\r\n<\/tr>\r\n
    Prefix<\/th>\r\nSymbol<\/th>\r\nFactor<\/th>\r\nExample<\/th>\r\n<\/tr>\r\n<\/thead>\r\n
    femto<\/td>\r\nf<\/td>\r\n10\u221215<\/sup><\/td>\r\n1 femtosecond (fs) = 1 \u00d7 10\u221215<\/sup> s (0.000000000000001 s)<\/td>\r\n<\/tr>\r\n
    pico<\/td>\r\np<\/td>\r\n10\u221212<\/sup><\/td>\r\n1 picometer (pm) = 1 \u00d7 10\u221212<\/sup> m (0.000000000001 m)<\/td>\r\n<\/tr>\r\n
    nano<\/td>\r\nn<\/td>\r\n10\u22129<\/sup><\/td>\r\n4 nanograms (ng) = 4 \u00d7 10\u22129<\/sup> g (0.000000004 g)<\/td>\r\n<\/tr>\r\n
    micro<\/td>\r\n\u00b5<\/td>\r\n10\u22126<\/sup><\/td>\r\n1 microliter (\u03bcL) = 1 \u00d7 10\u22126<\/sup> L (0.000001 L)<\/td>\r\n<\/tr>\r\n
    milli<\/td>\r\nm<\/td>\r\n10\u22123<\/sup><\/td>\r\n2 millimoles (mmol) = 2 \u00d7 10\u22123<\/sup> mol (0.002 mol)<\/td>\r\n<\/tr>\r\n
    centi<\/td>\r\nc<\/td>\r\n10\u22122<\/sup><\/td>\r\n7 centimeters (cm) = 7 \u00d7 10\u22122<\/sup> m (0.07 m)<\/td>\r\n<\/tr>\r\n
    deci<\/td>\r\nd<\/td>\r\n10\u22121<\/sup><\/td>\r\n1 deciliter (dL) = 1 \u00d7 10\u22121<\/sup> L (0.1 L )<\/td>\r\n<\/tr>\r\n
    kilo<\/td>\r\nk<\/td>\r\n103<\/sup><\/td>\r\n1 kilometer (km) = 1 \u00d7 103<\/sup> m (1000 m)<\/td>\r\n<\/tr>\r\n
    mega<\/td>\r\nM<\/td>\r\n106<\/sup><\/td>\r\n3 megahertz (MHz) = 3 \u00d7 106<\/sup> Hz (3,000,000 Hz)<\/td>\r\n<\/tr>\r\n
    giga<\/td>\r\nG<\/td>\r\n109<\/sup><\/td>\r\n8 gigayears (Gyr) = 8 \u00d7 109<\/sup> yr (8,000,000,000 yr)<\/td>\r\n<\/tr>\r\n
    tera<\/td>\r\nT<\/td>\r\n1012<\/sup><\/td>\r\n5 terawatts (TW) = 5 \u00d7 1012<\/sup> W (5,000,000,000,000 W)<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n

    SI Base Units<\/h2>\r\nThe initial units of the metric system, which eventually evolved into the SI system, were established in France during the French Revolution. The original standards for the meter and the kilogram were adopted there in 1799 and eventually by other countries. This section introduces four of the SI base units commonly used in chemistry. Other SI units will be introduced in subsequent chapters.\r\n

    Length<\/h3>\r\nThe standard unit of length<\/strong> in both the SI and original metric systems is the meter (m)<\/strong>. A meter was originally specified as 1\/10,000,000 of the distance from the North Pole to the equator. It is now defined as the distance light in a vacuum travels in 1\/299,792,458 of a second. A meter is about 3 inches longer than a yard (Figure\u00a01); one meter is about 39.37 inches or 1.094 yards. Longer distances are often reported in kilometers (1 km = 1000 m = 103<\/sup> m), whereas shorter distances can be reported in centimeters (1 cm = 0.01 m = 10\u22122<\/sup> m) or millimeters (1 mm = 0.001 m = 10\u22123<\/sup> m).\r\n\r\n[caption id=\"\" align=\"aligncenter\" width=\"881\"]\"One Figure\u00a01. The relative lengths of 1 m, 1 yd, 1 cm, and 1 in. are shown (not actual size), as well as comparisons of 2.54 cm and 1 in., and of 1 m and 1.094 yd.[\/caption]\r\n

    Mass<\/h3>\r\n[caption id=\"\" align=\"alignright\" width=\"250\"]\"The Figure\u00a02. This replica prototype kilogram is housed at the National Institute of Standards and Technology (NIST) in Maryland. (credit: National Institutes of Standards and Technology)[\/caption]\r\n\r\nThe standard unit of mass in the SI system is the kilogram (kg)<\/strong>. A kilogram was originally defined as the mass of a liter of water (a cube of water with an edge length of exactly 0.1 meter). It is now defined by a certain cylinder of platinum-iridium alloy, which is kept in France (Figure\u00a02). Any object with the same mass as this cylinder is said to have a mass of 1 kilogram. One kilogram is about 2.2 pounds. The gram (g) is exactly equal to 1\/1000 of the mass of the kilogram (10\u22123<\/sup> kg).\r\n

    Temperature<\/h3>\r\nTemperature is an intensive property. The SI unit of temperature is the kelvin (K)<\/strong>. The IUPAC convention is to use kelvin (all lowercase) for the word, K (uppercase) for the unit symbol, and neither the word \u201cdegree\u201d nor the degree symbol (\u00b0). The degree Celsius (\u00b0C) <\/strong>is also allowed in the SI system, with both the word \u201cdegree\u201d and the degree symbol used for Celsius measurements. Celsius degrees are the same magnitude as those of kelvin, but the two scales place their zeros in different places. Water freezes at 273.15 K (0 \u00b0C) and boils at 373.15 K (100 \u00b0C) by definition, and normal human body temperature is approximately 310 K (37 \u00b0C). The conversion between these two units and the Fahrenheit scale will be discussed later in this chapter.\r\n

    Time<\/h3>\r\nThe SI base unit of time is the second (s). Small and large time intervals can be expressed with the appropriate prefixes; for example, 3 microseconds = 0.000003 s = 3 \u00d7 10\u20136<\/sup> and 5 megaseconds = 5,000,000 s = 5 \u00d7 106<\/sup> s. Alternatively, hours, days, and years can be used.\r\n

    Derived SI Units<\/h2>\r\nWe can derive many units from the seven SI base units. For example, we can use the base unit of length to define a unit of volume, and the base units of mass and length to define a unit of density.\r\n

    Volume<\/h3>\r\nVolume<\/strong> is the measure of the amount of space occupied by an object. The standard SI unit of volume is defined by the base unit of length (Figure\u00a03). The standard volume is a cubic meter (m3<\/sup>)<\/strong>, a cube with an edge length of exactly one meter. To dispense a cubic meter of water, we could build a cubic box with edge lengths of exactly one meter. This box would hold a cubic meter of water or any other substance.\r\n\r\nA more commonly used unit of volume is derived from the decimeter (0.1 m, or 10 cm). A cube with edge lengths of exactly one decimeter contains a volume of one cubic decimeter (dm3<\/sup>). A liter (L) <\/strong> is the more common name for the cubic decimeter. One liter is about 1.06 quarts.\r\n\r\nA cubic centimeter (cm3<\/sup>)<\/strong> is the volume of a cube with an edge length of exactly one centimeter. The abbreviation cc<\/strong> (for c<\/strong>ubic c<\/strong>entimeter) is often used by health professionals. A cubic centimeter is also called a milliliter (mL)<\/strong> and is 1\/1000 of a liter.\r\n\r\n[caption id=\"\" align=\"aligncenter\" width=\"880\"]\"Figure\u00a0A Figure\u00a03. (a) The relative volumes are shown for cubes of 1 m3<\/sup>, 1 dm3<\/sup> (1 L), and 1 cm3<\/sup> (1 mL) (not to scale). (b) The diameter of a dime is compared relative to the edge length of a 1-cm3<\/sup> (1-mL) cube.[\/caption]\r\n

    Units not only are multiplied together but also can be divided. For example, if you are traveling at one meter for every second of time elapsed, your velocity is 1 meter per second, or 1 m\/s. The word per<\/em> implies division, so velocity is determined by dividing a distance quantity by a time quantity. Other units for velocity include kilometers per hour (km\/h) or even micrometers per nanosecond (\u03bcm\/ns). Later, we will see other derived units that can be expressed as fractions.<\/p>\r\n\r\n<\/div>\r\n

    \r\n
    \r\n
    \r\n

    Key Takeaways<\/h3>\r\n
      \r\n \t
    • Numbers tell \u201chow much,\u201d and units tell \u201cof what.\u201d<\/li>\r\n \t
    • Chemistry uses a set of fundamental units and derived units from SI units.<\/li>\r\n \t
    • Chemistry uses a set of prefixes that represent multiples or fractions of units.<\/li>\r\n \t
    • Units can be multiplied and divided to generate new units for quantities.<\/li>\r\n<\/ul>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n
      \r\n

      Exercises<\/h3>\r\n
        \r\n \t
      1. Is one liter about an ounce, a pint, a quart, or a gallon?<\/li>\r\n \t
      2. Is a meter about an inch, a foot, a yard, or a mile?<\/li>\r\n \t
      3. Indicate the SI base units or derived units that are appropriate for the following measurements:\r\n
          \r\n \t
        1. the length of a marathon race (26 miles 385 yards)<\/li>\r\n \t
        2. the mass of an automobile<\/li>\r\n \t
        3. the volume of a swimming pool<\/li>\r\n \t
        4. the speed of an airplane<\/li>\r\n \t
        5. the density of gold<\/li>\r\n \t
        6. the area of a football field<\/li>\r\n \t
        7. the maximum temperature at the South Pole on April 1, 1913<\/li>\r\n<\/ol>\r\n<\/li>\r\n \t
        8. Indicate the SI base units or derived units that are appropriate for the following measurements:\r\n
            \r\n \t
          1. the mass of the moon<\/li>\r\n \t
          2. the distance from Dallas to Oklahoma City<\/li>\r\n \t
          3. the speed of sound<\/li>\r\n \t
          4. the temperature at which alcohol boils<\/li>\r\n \t
          5. the volume of a flu shot or a measles vaccination<\/li>\r\n<\/ol>\r\n<\/li>\r\n \t
          6. Give the name and symbol of the prefixes used with SI units to indicate multiplication by the following exact quantities.\r\n
              \r\n \t
            1. 103<\/sup><\/li>\r\n \t
            2. 10\u22122<\/sup><\/li>\r\n \t
            3. 0.1<\/li>\r\n \t
            4. 10\u22123<\/sup><\/li>\r\n \t
            5. 1,000,000<\/li>\r\n \t
            6. 0.000001<\/li>\r\n<\/ol>\r\n<\/li>\r\n \t
            7. Give the name of the prefix and the quantity indicated by the following symbols that are used with SI base units.\r\n
                \r\n \t
              1. c<\/li>\r\n \t
              2. d<\/li>\r\n \t
              3. G<\/li>\r\n \t
              4. k<\/li>\r\n \t
              5. m<\/li>\r\n \t
              6. n<\/li>\r\n \t
              7. p<\/li>\r\n \t
              8. T<\/li>\r\n<\/ol>\r\n<\/li>\r\n<\/ol>\r\n[reveal-answer q=\"59360\"]Show Answers to Select Questions[\/reveal-answer]\r\n\r\n[hidden-answer a=\"59360\"]\r\n\r\n2. about a yard\r\n\r\n4. (a) kilograms; (b) meters; (c) kilometers\/second; (d) kelvin; (f) cubic meters\r\n\r\n6. (a) centi-, \u00d7 10\u22122<\/sup>; (b) deci-, \u00d7 10\u22121<\/sup>; (c) Giga-, \u00d7 109<\/sup>; (d) kilo-, \u00d7 103<\/sup>; (e) milli-, \u00d7 10\u22123<\/sup>; (f) nano-, \u00d7 10\u22129<\/sup>; (g) pico-, \u00d7 10\u221212<\/sup>; (h) tera-, \u00d7 1012<\/sup>\r\n\r\n[\/hidden-answer]\r\n\r\n<\/div>","rendered":"
                \n
                \n
                \n

                Learning Objectives<\/h3>\n
                  \n
                1. Learn the units that go with various quantities.<\/li>\n
                2. Express units using their abbreviations.<\/li>\n
                3. Make new units by combining numerical prefixes with units.<\/li>\n<\/ol>\n<\/div>\n<\/div>\n

                  A number indicates \u201chow much,\u201d but the unit indicates \u201cof what.\u201d The \u201cof what\u201d is important when communicating a quantity. For example, if you were to ask a friend how close you are to Lake Erie and your friend says \u201csix,\u201d then your friend isn\u2019t giving you complete information. Six what<\/em>? Six miles? Six inches? Six city blocks? The actual distance to the lake depends on what units you use.<\/p>\n

                  The number in the measurement can be represented in different ways, including decimal form and scientific notation. For example, the maximum takeoff weight of a Boeing 777 airliner is 298,000 kilograms, which can also be written as 2.98 \u00d7 105<\/sup> kg. The mass of the average mosquito is about 0.0000025 kilograms, which can be written as 2.5 \u00d7 10\u22126<\/sup> kg.<\/p>\n

                  Units<\/strong>, such as liters, pounds, and centimeters, are standards of comparison for measurements. When we buy a 2-liter bottle of a soft drink, we expect that the volume of the drink was measured, so it is two times larger than the volume that everyone agrees to be 1 liter. The meat used to prepare a 0.25-pound hamburger is measured so it weighs one-fourth as much as 1 pound. Without units, a number can be meaningless, confusing, or possibly life threatening. Suppose a doctor prescribes phenobarbital to control a patient\u2019s seizures and states a dosage of \u201c100\u201d without specifying units. Not only will this be confusing to the medical professional giving the dose, but the consequences can be dire: 100 mg given three times per day can be effective as an anticonvulsant, but a single dose of 100 g is more than 10 times the lethal amount.<\/p>\n

                  We usually report the results of scientific measurements in SI units, an updated version of the metric system, using the units listed in Table\u00a01. Other units can be derived from these base units. The standards for these units are fixed by international agreement, and they are called the International System of Units<\/strong> or SI Units <\/strong>(from the French, Le Syst\u00e8me International d\u2019Unit\u00e9s<\/em>). SI units have been used by the United States National Institute of Standards and Technology (NIST) since 1964.<\/p>\n\n\n\n\n\n\n\n\n\n\n
                  Table\u00a01. Base Units of the SI System<\/th>\n<\/tr>\n
                  Property Measured<\/th>\nName of Unit<\/th>\nSymbol of Unit<\/th>\n<\/tr>\n<\/thead>\n
                  length<\/td>\nmeter<\/td>\nm<\/td>\n<\/tr>\n
                  mass<\/td>\nkilogram<\/td>\nkg<\/td>\n<\/tr>\n
                  time<\/td>\nsecond<\/td>\ns<\/td>\n<\/tr>\n
                  temperature<\/td>\nkelvin<\/td>\nK<\/td>\n<\/tr>\n
                  amount of substance<\/td>\nmole<\/td>\nmol<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

                  Sometimes we use units that are fractions or multiples of a base unit. Ice cream is sold in quarts (a familiar, non-SI base unit), pints (0.5 quart), or gallons (4 quarts). We also use fractions or multiples of units in the SI system, but these fractions or multiples are always powers of 10. Fractional or multiple SI units are named using a prefix and the name of the base unit. For example, a length of 1000 meters is also called a kilometer because the prefix kilo<\/em> means \u201cone thousand,\u201d which in scientific notation is 103<\/sup> (1 kilometer = 1000 m = 103<\/sup> m). The prefixes used and the powers to which 10 are raised are listed in Table\u00a02.<\/p>\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
                  Table\u00a02. Common Unit Prefixes<\/th>\n<\/tr>\n
                  Prefix<\/th>\nSymbol<\/th>\nFactor<\/th>\nExample<\/th>\n<\/tr>\n<\/thead>\n
                  femto<\/td>\nf<\/td>\n10\u221215<\/sup><\/td>\n1 femtosecond (fs) = 1 \u00d7 10\u221215<\/sup> s (0.000000000000001 s)<\/td>\n<\/tr>\n
                  pico<\/td>\np<\/td>\n10\u221212<\/sup><\/td>\n1 picometer (pm) = 1 \u00d7 10\u221212<\/sup> m (0.000000000001 m)<\/td>\n<\/tr>\n
                  nano<\/td>\nn<\/td>\n10\u22129<\/sup><\/td>\n4 nanograms (ng) = 4 \u00d7 10\u22129<\/sup> g (0.000000004 g)<\/td>\n<\/tr>\n
                  micro<\/td>\n\u00b5<\/td>\n10\u22126<\/sup><\/td>\n1 microliter (\u03bcL) = 1 \u00d7 10\u22126<\/sup> L (0.000001 L)<\/td>\n<\/tr>\n
                  milli<\/td>\nm<\/td>\n10\u22123<\/sup><\/td>\n2 millimoles (mmol) = 2 \u00d7 10\u22123<\/sup> mol (0.002 mol)<\/td>\n<\/tr>\n
                  centi<\/td>\nc<\/td>\n10\u22122<\/sup><\/td>\n7 centimeters (cm) = 7 \u00d7 10\u22122<\/sup> m (0.07 m)<\/td>\n<\/tr>\n
                  deci<\/td>\nd<\/td>\n10\u22121<\/sup><\/td>\n1 deciliter (dL) = 1 \u00d7 10\u22121<\/sup> L (0.1 L )<\/td>\n<\/tr>\n
                  kilo<\/td>\nk<\/td>\n103<\/sup><\/td>\n1 kilometer (km) = 1 \u00d7 103<\/sup> m (1000 m)<\/td>\n<\/tr>\n
                  mega<\/td>\nM<\/td>\n106<\/sup><\/td>\n3 megahertz (MHz) = 3 \u00d7 106<\/sup> Hz (3,000,000 Hz)<\/td>\n<\/tr>\n
                  giga<\/td>\nG<\/td>\n109<\/sup><\/td>\n8 gigayears (Gyr) = 8 \u00d7 109<\/sup> yr (8,000,000,000 yr)<\/td>\n<\/tr>\n
                  tera<\/td>\nT<\/td>\n1012<\/sup><\/td>\n5 terawatts (TW) = 5 \u00d7 1012<\/sup> W (5,000,000,000,000 W)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

                  SI Base Units<\/h2>\n

                  The initial units of the metric system, which eventually evolved into the SI system, were established in France during the French Revolution. The original standards for the meter and the kilogram were adopted there in 1799 and eventually by other countries. This section introduces four of the SI base units commonly used in chemistry. Other SI units will be introduced in subsequent chapters.<\/p>\n

                  Length<\/h3>\n

                  The standard unit of length<\/strong> in both the SI and original metric systems is the meter (m)<\/strong>. A meter was originally specified as 1\/10,000,000 of the distance from the North Pole to the equator. It is now defined as the distance light in a vacuum travels in 1\/299,792,458 of a second. A meter is about 3 inches longer than a yard (Figure\u00a01); one meter is about 39.37 inches or 1.094 yards. Longer distances are often reported in kilometers (1 km = 1000 m = 103<\/sup> m), whereas shorter distances can be reported in centimeters (1 cm = 0.01 m = 10\u22122<\/sup> m) or millimeters (1 mm = 0.001 m = 10\u22123<\/sup> m).<\/p>\n

                  \"One<\/p>\n

                  Figure\u00a01. The relative lengths of 1 m, 1 yd, 1 cm, and 1 in. are shown (not actual size), as well as comparisons of 2.54 cm and 1 in., and of 1 m and 1.094 yd.<\/p>\n<\/div>\n

                  Mass<\/h3>\n
                  \"The<\/p>\n

                  Figure\u00a02. This replica prototype kilogram is housed at the National Institute of Standards and Technology (NIST) in Maryland. (credit: National Institutes of Standards and Technology)<\/p>\n<\/div>\n

                  The standard unit of mass in the SI system is the kilogram (kg)<\/strong>. A kilogram was originally defined as the mass of a liter of water (a cube of water with an edge length of exactly 0.1 meter). It is now defined by a certain cylinder of platinum-iridium alloy, which is kept in France (Figure\u00a02). Any object with the same mass as this cylinder is said to have a mass of 1 kilogram. One kilogram is about 2.2 pounds. The gram (g) is exactly equal to 1\/1000 of the mass of the kilogram (10\u22123<\/sup> kg).<\/p>\n

                  Temperature<\/h3>\n

                  Temperature is an intensive property. The SI unit of temperature is the kelvin (K)<\/strong>. The IUPAC convention is to use kelvin (all lowercase) for the word, K (uppercase) for the unit symbol, and neither the word \u201cdegree\u201d nor the degree symbol (\u00b0). The degree Celsius (\u00b0C) <\/strong>is also allowed in the SI system, with both the word \u201cdegree\u201d and the degree symbol used for Celsius measurements. Celsius degrees are the same magnitude as those of kelvin, but the two scales place their zeros in different places. Water freezes at 273.15 K (0 \u00b0C) and boils at 373.15 K (100 \u00b0C) by definition, and normal human body temperature is approximately 310 K (37 \u00b0C). The conversion between these two units and the Fahrenheit scale will be discussed later in this chapter.<\/p>\n

                  Time<\/h3>\n

                  The SI base unit of time is the second (s). Small and large time intervals can be expressed with the appropriate prefixes; for example, 3 microseconds = 0.000003 s = 3 \u00d7 10\u20136<\/sup> and 5 megaseconds = 5,000,000 s = 5 \u00d7 106<\/sup> s. Alternatively, hours, days, and years can be used.<\/p>\n

                  Derived SI Units<\/h2>\n

                  We can derive many units from the seven SI base units. For example, we can use the base unit of length to define a unit of volume, and the base units of mass and length to define a unit of density.<\/p>\n

                  Volume<\/h3>\n

                  Volume<\/strong> is the measure of the amount of space occupied by an object. The standard SI unit of volume is defined by the base unit of length (Figure\u00a03). The standard volume is a cubic meter (m3<\/sup>)<\/strong>, a cube with an edge length of exactly one meter. To dispense a cubic meter of water, we could build a cubic box with edge lengths of exactly one meter. This box would hold a cubic meter of water or any other substance.<\/p>\n

                  A more commonly used unit of volume is derived from the decimeter (0.1 m, or 10 cm). A cube with edge lengths of exactly one decimeter contains a volume of one cubic decimeter (dm3<\/sup>). A liter (L) <\/strong> is the more common name for the cubic decimeter. One liter is about 1.06 quarts.<\/p>\n

                  A cubic centimeter (cm3<\/sup>)<\/strong> is the volume of a cube with an edge length of exactly one centimeter. The abbreviation cc<\/strong> (for c<\/strong>ubic c<\/strong>entimeter) is often used by health professionals. A cubic centimeter is also called a milliliter (mL)<\/strong> and is 1\/1000 of a liter.<\/p>\n

                  \"Figure\u00a0A<\/p>\n

                  Figure\u00a03. (a) The relative volumes are shown for cubes of 1 m3<\/sup>, 1 dm3<\/sup> (1 L), and 1 cm3<\/sup> (1 mL) (not to scale). (b) The diameter of a dime is compared relative to the edge length of a 1-cm3<\/sup> (1-mL) cube.<\/p>\n<\/div>\n

                  Units not only are multiplied together but also can be divided. For example, if you are traveling at one meter for every second of time elapsed, your velocity is 1 meter per second, or 1 m\/s. The word per<\/em> implies division, so velocity is determined by dividing a distance quantity by a time quantity. Other units for velocity include kilometers per hour (km\/h) or even micrometers per nanosecond (\u03bcm\/ns). Later, we will see other derived units that can be expressed as fractions.<\/p>\n<\/div>\n

                  \n
                  \n
                  \n

                  Key Takeaways<\/h3>\n