<p>By the end of this lesson and the next few, you should be able to:</p>
<ul>
<li>Explain the process of measurement</li>
<li>Identify the three basic parts of a quantity</li>
<li>Describe the properties and units of length, mass, volume, density, temperature, and time</li>
<li>Perform basic unit calculations and conversions in the metric and other unit systems</li>
</ul>
<h2>What are measurements?</h2>
<p id="fs-idm75764096">Measurements provide the macroscopic information that is the basis of most of the hypotheses, theories, and laws that describe the behavior of matter and <a data-lesson="energy" data-subject="chemistry" data-tutorial="thermochemistry" href="https://app.ulearngo.com/chemistry/thermochemistry/energy">energy</a> in both the macroscopic and microscopic domains of chemistry.</p>
<p>Every measurement provides three kinds of information: the size or magnitude of the measurement (a number); a standard of comparison for the measurement (a unit); and an indication of the <a data-lesson="heisenberg-uncertainty-principle" data-subject="chemistry" data-tutorial="electronic-structure-of-atoms" href="https://app.ulearngo.com/chemistry/electronic-structure-of-atoms/heisenberg-uncertainty-principle">uncertainty</a> of the measurement. While the number and unit are explicitly represented when a quantity is written, the uncertainty is an aspect of the measurement result that is more implicitly represented and will be discussed later.</p>
<p id="fs-idm128012432">The number in the measurement can be represented in different ways, including decimal form and scientific notation. Scientific notation is also known as exponential notation, which is a mathematical concept. For example, the maximum takeoff weight of a Boeing 777-200ER airliner is 298,000 kilograms, which can also be written as 2.98 × 10<sup>5</sup> kg. The <a data-lesson="molar-mass" data-subject="chemistry" data-tutorial="quantitative-aspects-chemical-change" href="https://app.ulearngo.com/chemistry/quantitative-aspects-chemical-change/molar-mass">mass</a> of the average mosquito is about 0.0000025 kilograms, which can be written as 2.5 × 10<sup>−6</sup> kg.</p>
<h3>Units</h3>
<p id="fs-idp178656"><strong>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 <a data-lesson="volume-and-temperature-charless-law" data-subject="chemistry" data-tutorial="gases" href="https://app.ulearngo.com/chemistry/gases/volume-and-temperature-charless-law">volume</a> 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.</p>
<p>Without units, a number can be meaningless, confusing, or possibly life threatening. Suppose a doctor prescribes phenobarbital to <a data-lesson="control-rods" data-subject="chemistry" data-tutorial="nuclear-chemistry" href="https://app.ulearngo.com/chemistry/nuclear-chemistry/control-rods">control</a> a patient’s seizures and states a dosage of “100” 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>
<h3>SI Units</h3>
<p id="fs-idm144392592">We usually report the results of scientific measurements in SI units, an updated version of the metric system, using the units listed in the table below. Other units can be derived from these base units.</p>
<p>The standards for these units are fixed by international agreement, and they are called the <strong>International System of Units</strong> or <strong>SI Units</strong> (from the French, <em data-effect="italics">Le Système International d’Unités</em>). SI units have been used by the United States National Institute of Standards and Technology (NIST) since 1964.</p>
<table class="span-all" id="fs-idm81346144" summary="Length is measured with the meter, which is symbolized using a lowercase M. Mass is measured with the kilogram which is symbolized with a lowercase K G. Time is measured with the second, which is symbolized with a lowercase S. Temperature is measured with the kelvin which is symbolized with an uppercase K. Electric current is measured with the ampere which is symbolized with an uppercase A. The amount of a substance is measured with the mole, which is symbolized with the lowercase letters, M O L. Luminous intensity is measured with the candela, which is symbolized with the lowercase letters C D.">
<thead>
<tr>
<th colspan="3" data-align="center" scope="col">
<h3>Base Units of the SI System</h3>
</th>
</tr>
<tr valign="top">
<th data-align="left" scope="col">Property Measured</th>
<th data-align="left" scope="col">Name of Unit</th>
<th data-align="left" scope="col">Symbol of Unit</th>
</tr>
</thead>
<tbody>
<tr valign="top">
<td data-align="left">length</td>
<td data-align="left">meter</td>
<td data-align="left">m</td>
</tr>
<tr valign="top">
<td data-align="left">mass</td>
<td data-align="left">kilogram</td>
<td data-align="left">kg</td>
</tr>
<tr valign="top">
<td data-align="left">time</td>
<td data-align="left">second</td>
<td data-align="left">s</td>
</tr>
<tr valign="top">
<td data-align="left">temperature</td>
<td data-align="left">kelvin</td>
<td data-align="left">K</td>
</tr>
<tr valign="top">
<td data-align="left">electric current</td>
<td data-align="left">ampere</td>
<td data-align="left">A</td>
</tr>
<tr valign="top">
<td data-align="left">amount of substance</td>
<td data-align="left">mole</td>
<td data-align="left">mol</td>
</tr>
<tr valign="top">
<td data-align="left">luminous intensity</td>
<td data-align="left">candela</td>
<td data-align="left">cd</td>
</tr>
</tbody>
</table>
<h3>Unit Prefixes</h3>
<p>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.</p>
<p>For example, a length of 1000 meters is also called a kilometer because the prefix <em data-effect="italics">kilo</em> means “one thousand,” which in scientific notation is 10<sup>3</sup> (1 kilometer = 1000 m = 10<sup>3</sup> m). The prefixes used and the powers to which 10 are raised are listed in the table below.</p>
<table class="span-all" id="fs-idm81128320" summary="The prefix femto has the symbol lowercase f and a factor of 10 to the negative fifteenth power. Therefore, 1 femtosecond, F S, is equal to 1 times 10 to the negative 15 of a meter, or 0.000000000001 of a meter. The prefix pico has the symbol lowercase P and a factor of 10 to the negative twelfth power. Therefore, 1 picosecond, P S, is equal to 1 times 10 to the negative 12 of a meter, or 0.000000000001 of a meter. The prefix nano has the symbol lowercase N and a factor of 10 to the negative ninth power. Therefore, 4 nanograms, or NG, equals 4 times ten to the negative 9, or 0.000000004 g. The prefix micro has the greek letter mu as its symbol and a factor of 10 to the negative sixth power. Therefore, 1 microliter, or mu L, is equal to one times ten to the negative 6 or 0.000001 L. The prefix milli has a lowercase M as its symbol and a factor of 10 to the negative third power. Therefore, 2 millimoles, or M mol, are equal to two times ten to the negative 3 or 0.002 mol. The prefix centi has a lowercase C as its symbol and a factor of 10 to the negative second power. Therefore, 7 centimeters, or C M, are equal to seven times ten to the negative 2 meters or 0.07 M O L. The prefix deci has a lowercase D as its symbol and a factor of 10 to the negative first power. Therefore, 1 deciliter, or lowercase D uppercase L, are equal to one times ten to the negative 1 meters or 0.1 L. The prefix kilo has a lowercase K as its symbol and a factor of 10 to the third power. Therefore, 1 kilometer, or K M, is equal to one times ten to the third meters or 1000 M. The prefix mega has an uppercase M as its symbol and a factor of 10 to the sixth power. Therefore, 3 megahertz, or M H Z, are equal to three times 10 to the sixth hertz, or 3000000 H Z. The prefix giga has an uppercase G as its symbol and a factor of 10 to the ninth power. Therefore, 8 gigayears, or G Y R, are equal to eight times 10 to the ninth years, or 800000000 G Y R. The prefix tera has an uppercase T as its symbol and a factor of 10 to the twelfth power. Therefore, 5 terawatts, or T W, are equal to five times 10 to the twelfth watts, or 5000000000000 W.">
<thead>
<tr>
<th colspan="4" data-align="center" scope="col">Common Unit Prefixes</th>
</tr>
<tr valign="top">
<th data-align="left" scope="col">Prefix</th>
<th data-align="left" scope="col">Symbol</th>
<th data-align="left" scope="col">Factor</th>
<th data-align="left" scope="col">Example</th>
</tr>
</thead>
<tbody>
<tr valign="top">
<td data-align="left">femto</td>
<td data-align="left">f</td>
<td data-align="left">10<sup>−15</sup></td>
<td data-align="left">1 femtosecond (fs) = 1 × 10<sup>−15</sup> s (0.000000000000001 s)</td>
</tr>
<tr valign="top">
<td data-align="left">pico</td>
<td data-align="left">p</td>
<td data-align="left">10<sup>−12</sup></td>
<td data-align="left">1 picometer (pm) = 1 × 10<sup>−12</sup> m (0.000000000001 m)</td>
</tr>
<tr valign="top">
<td data-align="left">nano</td>
<td data-align="left">n</td>
<td data-align="left">10<sup>−9</sup></td>
<td data-align="left">4 nanograms (ng) = 4 × 10<sup>−9</sup> g (0.000000004 g)</td>
</tr>
<tr valign="top">
<td data-align="left">micro</td>
<td data-align="left">µ</td>
<td data-align="left">10<sup>−6</sup></td>
<td data-align="left">1 microliter (μL) = 1 × 10<sup>−6</sup> L (0.000001 L)</td>
</tr>
<tr valign="top">
<td data-align="left">milli</td>
<td data-align="left">m</td>
<td data-align="left">10<sup>−3</sup></td>
<td data-align="left">2 millimoles (mmol) = 2 × 10<sup>−3</sup> mol (0.002 mol)</td>
</tr>
<tr valign="top">
<td data-align="left">centi</td>
<td data-align="left">c</td>
<td data-align="left">10<sup>−2</sup></td>
<td data-align="left">7 centimeters (cm) = 7 × 10<sup>−2</sup> m (0.07 m)</td>
</tr>
<tr valign="top">
<td data-align="left">deci</td>
<td data-align="left">d</td>
<td data-align="left">10<sup>−1</sup></td>
<td data-align="left">1 deciliter (dL) = 1 × 10<sup>−1</sup> L (0.1 L )</td>
</tr>
<tr valign="top">
<td data-align="left">kilo</td>
<td data-align="left">k</td>
<td data-align="left">10<sup>3</sup></td>
<td data-align="left">1 kilometer (km) = 1 × 10<sup>3</sup> m (1000 m)</td>
</tr>
<tr valign="top">
<td data-align="left">mega</td>
<td data-align="left">M</td>
<td data-align="left">10<sup>6</sup></td>
<td data-align="left">3 megahertz (MHz) = 3 × 10<sup>6</sup> Hz (3,000,000 Hz)</td>
</tr>
<tr valign="top">
<td data-align="left">giga</td>
<td data-align="left">G</td>
<td data-align="left">10<sup>9</sup></td>
<td data-align="left">8 gigayears (Gyr) = 8 × 10<sup>9</sup> yr (8,000,000,000 Gyr)</td>
</tr>
<tr valign="top">
<td data-align="left">tera</td>
<td data-align="left">T</td>
<td data-align="left">10<sup>12</sup></td>
<td data-align="left">5 terawatts (TW) = 5 × 10<sup>12</sup> W (5,000,000,000,000 W)</td>
</tr>
</tbody>
</table>

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Measurements and SI System

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Measurements and SI System

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