Name: measurement: si units and conversions
Uploaded: 2020-09-03T13:38:25.000Z
Duration: 3 min 38 s
Channel: JoVE

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Ohio’s Learning Standards and Model Curriculum

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Chemistry

Structure And Properties Of Matter

Quantifying matter

Measurement: Standard Units

In science, measurement is the assignment of a numerical value to a characteristic, like the mass, size, and temperature of the matter.

Every measurement provides two kinds of information. The first is the number &#8211; the size or magnitude of the measurement. The second is the unit &#8211; a standard of comparison for the measurement.

So, when water boils at 100 &#176;C, the number 100 represents the magnitude of measurement, and &#176;C represents the unit. Together, they convey the relative size of the property of the matter in question &#8211; the boiling point.

Without units, a number can be meaningless or confusing. For example, if the height of the Eiffel Tower is reported to be 300, without providing units the context of this 300 number is unclear. This means the Eiffel tower could be relatively tall, or very short, but without the units to compare, this makes that difficult to assess.

Sometimes, a third form of information, error, is also provided. These data are an indication of the uncertainty of the measurement.

Thus, in order to measure and report the various properties of matter accurately, common systems of measurement have been developed. The International System of Units or the SI system is the one used by scientists universally.

Under the SI system, measurement units for 7 fundamental properties &#8212; length, mass, time, temperature, electric current, amount of substance, and luminous intensity &#8212; have been fixed. These are called the Standard Units, or the base units. Of these, the base units for the first four properties are the most commonly used in chemistry.

The standard unit of length in the SI system is the meter, represented by the unit symbol &#8220;m&#8221;. Longer distances are often reported in kilometers, or &#8220;km&#8221;, where 1 kilometer is equal to 1000 meters. Conversely, shorter distances can be reported in centimeters, or &#8220;cm&#8221;, where 1 centimeter is equal to 0.01 meters; or millimeters, &#8220;mm&#8221;, where 1 millimeter is equal to 0.001 meters.

Similarly, the standard unit of mass in the SI system is the kilogram, represented by the unit symbol &#8220;kg&#8221;. A kilogram is equal to 1000 grams.

Temperature is another fundamental property, with the SI unit kelvin, and the unit symbol &#8220;K&#8221; in uppercase. This is displayed without the word &#8220;degree&#8221; or the symbol degree, to distinguish it from degrees Celsius and degrees Fahrenheit. For example, water boils at 373.15 K, and normal human body temperature is approximately 310 K.

The fourth most commonly used base unit is second, the SI unit of time, with the unit symbol &#8220;s&#8221;. While shorter time intervals can be expressed as milliseconds, where 1 millisecond is equal to 0.001 seconds, longer time intervals can be expressed as megaseconds where 1 megasecond is equal to 1 million seconds. Alternatively, non-SI units like hours, days, and years are also used.

measurement: standard units

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 uncertainty of the measurement. While the number and unit are explicitly represented when a quantity is written, the uncertainty is an aspect of the errors in the measurement results.

The number in the measurement can be represented in different ways, including decimal form and scientific notation, which is also known as exponential notation. For example, the maximum take-off weight of a Boeing 777-200ER airliner is 298,000 kilograms, which can also be written as 2.98 &#215; 105 kg. 

Units, such as liters, pounds, and centimeters, are standards of comparison for measurements. A 2-liter bottle of a soft drink contains a volume of beverage that is twice that of the accepted volume of 1 liter. Without units, a number can be meaningless, confusing, or possibly life-threatening. Suppose a doctor prescribes phenobarbital to control a patient&#8217;s seizures and states a dosage of &#8220;100&#8221; 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.

<h4>The International System of Units (SI Units)</h4>

The measurement units for seven fundamental properties (&#8220;base units&#8221;): length, mass, time, temperature, electric current, amount of substance, and luminous intensity, have been fixed by international agreement. They are called the International System of Units or SI Units. Units for other properties may be derived from these seven base units. Everyday measurement units are often defined as fractions or multiples of other units. Milk is commonly packaged in containers of 1 gallon (4 quarts), 1 quart (0.25 gallons), and one pint (0.5 quarts. This same approach is used with SI units, 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 means &#8220;one thousand,&#8221; which in scientific notation is 103 (1 kilometer = 1000 m = 103 m).

<h4>Standard SI Units</h4>

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. The following are the four SI base units commonly used in chemistry.

<h4>1. Length</h4>

The standard unit of length in the SI system is the meter (m). A meter is defined as the distance light travels in a vacuum in 1/299,792,458 of a second. Longer distances are often reported in kilometers (1 km = 1000 m = 103 m), whereas shorter distances can be reported in centimeters (1 cm = 0.01 m = 10&#8722;2 m) or millimeters (1 mm = 0.001 m = 10&#8722;3 m).

<h4>2. Mass</h4>

The standard unit of mass in the SI system is the kilogram (kg). A kilogram is defined by the mass of a reference object - a metal cylinder made from platinum-iridium alloy with a height and diameter of 39 mm. Any object with the same mass as this reference is said to have a mass of 1 kilogram. The gram (g) is exactly equal to 1/1000 of the mass of the kilogram (10&#8722;3 kg).

The term &#8220;weight&#8221; is often used interchangeably with &#8220;mass.&#8221; However, the two quantities are different. While the mass of an object measures the quantity of matter within it, its weight measures the gravitational force exerted on its matter. For instance, if we could weigh ourselves on the moon, which has weaker gravity than Earth, we would weigh less than we did on Earth. However, mass&#8212;the quantity of matter in our body&#8212;would stay the same.

<h4>3. Temperature</h4>

The SI unit of temperature is the kelvin (K), although the degree Celsius (&#176;C) is also allowed in the SI system, with both the word &#8220;degree&#8221; 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 &#176;C) and boils at 373.15 K (100 &#176;C) by definition, and normal human body temperature is approximately 310 K (37 &#176;C). The Fahrenheit (&#176;F) scale is another commonly used unit for measuring temperature. On the Fahrenheit scale, water freezes at 32 &#176;F and boils at 212 &#176;F, and the normal human body temperature is 96 &#176;F. 

While Fahrenheit and Celsius scales allow for negative temperatures, the Kelvin scale, also called the absolute scale, does not. On the Kelvin scale, 0 K is the lowest temperature, which is known as absolute zero. 

The temperature scales are interconvertible using the following conversion formulas:

<img alt="Temperature conversion formula, Celsius from Fahrenheit, equation." src="/files/core/CDNSource/lessons/1010/1010_Equations-01.png" style="height: 40px;" data-altupdatedat="1761830439000" data-alt="Eq1" />

<img alt="Temperature conversion formula; Celsius to Kelvin equation T(K)=T(&#176;C)+273.15, educational use." src="/files/core/CDNSource/lessons/1010/1010_Equations-02.png" style="height: 40px;" data-altupdatedat="1761830439000" data-alt="Eq2" />

<h4>4. Time</h4>

The SI base unit of time is the second (s). Small and large time intervals can be expressed with the appropriate prefixes. For example: 

<img alt="Conversion of 5 megaseconds in scientific notation; formula representation." src="/files/core/CDNSource/lessons/1010/1010_Equations-03.png" style="height: 40px;" data-altupdatedat="1761830439000" data-alt="Eq3" />

<img alt="Converting time units: 3 microseconds equals 0.000003 s or 3 &#215; 10&#8315;&#8310; s; equation illustration." src="/files/core/CDNSource/lessons/1010/1010_Equations-04.png" style="height: 40px;" data-altupdatedat="1761830439000" data-alt="Eq4" />

Alternatively, hours, days, and years can be used.

This text is adapted from <a href="https://openstax.org/books/chemistry-2e/pages/1-4-measurements">Openstax, Chemistry 2e, Section 1.4: Measurements.</a>

Every measurement provides three kinds of information: the size or magnitude of the measurement (a number), a standard of comparison for the measurement ...

Education

JoVE Core

Introduction: Matter and Measurement

KEY TERMS AND CONCEPTS

measurement: si units and conversions

Measurement gives three kinds of information: a number, a unit, and an estimate of uncertainty. The number shows size or magnitude. The unit gives a standard for comparison. The uncertainty reflects possible error in the measurement.

Numbers can be written in more than one way. A value may appear in decimal form or in scientific notation, which is also called exponential notation. For example, the maximum take-off weight of a Boeing 777-200ER airliner is 298,000 kilograms, or 2.98 × 10^5 kg.

Units are essential because they make a number meaningful. Common units such as liters, pounds, and centimeters help people compare measurements. A 2-liter bottle of soft drink contains twice the volume of a 1-liter bottle. Without units, a number can be confusing or even dangerous. A doctor who writes a dose as “100” without units could create a serious mistake, because 100 mg taken three times a day can be effective, while 100 g is more than 10 times the lethal amount.

The International System of Units, or SI units, is based on seven fundamental properties called base units. These properties are length, mass, time, temperature, electric current, amount of substance, and luminous intensity. Other units are derived from these base units. Everyday units often use fractions or multiples of a base unit, and SI units do the same with powers of 10. Prefixes show these multiples. For example, kilo means one thousand, so 1 kilometer equals 1000 meters, or 10^3 m.

The metric system began in France during the French Revolution. The original standards for the meter and kilogram were adopted in 1799 and later used by other countries. In chemistry, the four SI base units used most often are length, mass, temperature, and time.

The SI unit of length is the meter, or m. A meter is defined as the distance light travels in a vacuum in 1/299,792,458 of a second. Longer distances are often given in kilometers, while shorter distances are often given in centimeters or millimeters. These units relate directly to the meter: 1 km = 1000 m = 10^3 m, 1 cm = 0.01 m = 10^-2 m, and 1 mm = 0.001 m = 10^-3 m.

The SI unit of mass is the kilogram, or kg. It is defined by a reference object, a metal cylinder made from platinum-iridium alloy with a height and diameter of 39 mm. Any object with the same mass as that reference has a mass of 1 kilogram. The gram, or g, is exactly 1/1000 of a kilogram, which is 10^-3 kg. Weight is often used like mass, but they are not the same. Mass is the amount of matter in an object, while weight is the gravitational force on that matter. That is why a person would weigh less on the moon, where gravity is weaker, but the mass would stay the same.

The SI unit of temperature is the kelvin, or K, although degree Celsius, or °C, is also allowed in SI. Celsius and kelvin have the same size unit, but their zero points are different. Water freezes at 273.15 K, which is 0 °C, and boils at 373.15 K, which is 100 °C. Normal human body temperature is about 310 K, or 37 °C. Fahrenheit, or °F, is another common scale. On that scale, water freezes at 32 °F and boils at 212 °F, and normal body temperature is 96 °F. Celsius and Fahrenheit can show negative temperatures, but Kelvin cannot. The Kelvin scale starts at 0 K, called absolute zero. Temperature scales can be converted using the given formulas.

The SI base unit of time is the second, or s. Small and large time intervals can be written with prefixes, and hours, days, and years are also used. Together, these units help scientists and students describe measurements clearly and compare results with confidence.

Measurement: SI Units and Conversions

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Measurement: SI Units and Conversions | JoVE K12

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The Bohr Model

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Atomic structure
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• Polar/covalent

Content elaboration: Content in the Physical Science course included recognizing that atoms with unpaired electrons tend to form ionic and covalent bonds with other atoms, forming molecules, ionic lattices or network covalent structures. In this course, electron configuration, electronegativity values and energy considerations will be applied to bonding and the properties of materials with different types of bonding. Atoms of many elements are more stable when they are bonded to other atoms. In such cases, as atoms bond, energy is released to the surroundings, resulting in a system with lower energy. An atom's electron configuration, particularly the valence electrons, determines how an atom interacts with other atoms. Molecules, ionic lattices and network covalent structures have different, yet predictable, properties that depend on the identity of the elements and the types of bonds formed. Differences in electronegativity values can be used to predict where a bond fits on the continuum between ionic and covalent bonds. The polarity of a bond depends on the electronegativity difference and the distance between the atoms (bond length). Polar covalent bonds are introduced as an intermediary between ionic and pure covalent bonds. The concept of metallic bonding is also introduced to explain many of the properties of metals (e.g., conductivity). Since most compounds contain multiple bonds, a substance may contain more than one type of bond. Carbon atoms can bond together and with other atoms, especially hydrogen, oxygen, nitrogen and sulfur, to form chains, rings and branching networks that are present in a variety of important compounds, including synthetic polymers, fossil fuels and the large molecules essential to life.

Chemical bonding

Chemical Formulas

A chemical formula presents information about the proportions of atoms constituting a particular chemical compound or molecule, mainly using symbols of ...

ionic-compounds-formulas-and-nomenclature

Ionic Compounds: Formulas and Nomenclature

An element composed of atoms that readily lose electrons (a metal) can react with an element composed of atoms that readily gain electrons (a nonmetal) to ...

molecular-compounds-formulas-and-nomenclature

Molecular Compounds: Formulas and Nomenclature

Molecular compounds or covalent compounds result when atoms share electrons to form covalent bonds. Since there is no electron transfer, molecular ...

Organic Compounds

All living things are formed mostly of carbon compounds called organic compounds. The category of organic compounds includes both natural and synthetic ...

Classification of Elements and Compounds

Pure substances consist of only one type of matter. A pure substance can be an element or a compound. An element consists of only one type of atom, while ...

Molecular Models

Physical models representing molecular architectures of chemical compounds play essential roles in understanding chemistry. The use of molecular models ...

Representing compounds
• Formula writing
• Nomenclature
• Models and shapes (Lewis structures, ball and stick, molecular geometries)

Content elaboration: Using the periodic table, formulas of ionic compounds containing specific elements can be predicted. This can include ionic compounds made up of elements from groups 1, 2, 17, hydrogen, oxygen and polyatomic ions (given the formula and charge of the polyatomic ion). Given the formula, a compound can be named using conventional systems that include Greek prefixes and Roman numerals where appropriate. Given the name of an ionic or covalent substance, formulas can be written. Many different models can be used to represent compounds including chemical formulas, Lewis structures, and ball and stick models. These models can be used to visualize atoms and molecules and to predict the properties of substances. Each type of representation provides unique information about the compound. Different representations are better suited for particular substances. Lewis structures can be drawn to represent covalent compounds using a simple set of rules and can be combined with valence shell electron pair repulsion (VSEPR) theory to predict the three-dimensional electron pair and molecular geometry of compounds. Lewis structures and molecular geometries will only be constructed for the following combination of elements: hydrogen, carbon, nitrogen, oxygen, phosphorus, sulfur and the halogens.

Representing compounds

Measurement: Derived Units

The International System of Units or SI system, by international agreement, has fixed measurement units for seven fundamental properties: length, mass, ...

Uncertainty in Measurement: Accuracy and Precision

Scientists typically make repeated measurements of a quantity to ensure the quality of their findings and to evaluate both the precision and the accuracy ...

Uncertainty in Measurement: Reading Instruments

Counting is the type of measurement that is free from uncertainty, provided the number of objects being counted does not change during the process. Such ...

Uncertainty in Measurement: Significant Figures

All the digits in a measurement, including the uncertain last digit, are called significant figures or significant digits. Note that zero may be a ...

Dimensional Analysis

Dimensional analysis, also known as the factor label method, is a versatile approach for mathematical operations. The main principle behind this approach ...

Elements: Chemical Symbols and Isotopes

A chemical symbol is an abbreviation used to indicate an element or an atom of an element. For example, the symbol for mercury is Hg. The same symbol is ...

Atomic Mass

Atoms &mdash; and the protons, neutrons, and electrons that compose them &mdash; are extremely small. For example, a carbon atom weighs less than 2 ...

Molar Mass

The identity of a substance is defined not only by the types of atoms or ions it contains but by the quantity of each type of atom or ion. For example, ...

Quantifying matter

Content elaboration: In earlier grades, properties of materials were quantified with measurements that were always associated with some error. In this course, scientific protocols for quantifying the properties of matter accurately and precisely are studied. Using the International System of Units (SI), significant digits or figures, scientific notation, error analysis and dimensional analysis are vital to scientific communication. There are three domains of magnitude in size and time: the macroscopic (human) domain, the cosmic domain and the submicroscopic (atomic and subatomic) domain. Measurements in the cosmic domain and submicroscopic domains require complex instruments and/or procedures. Matter can be quantified in a way that macroscopic properties such as mass can reflect the number of particles present. Elemental samples are a mixture of several isotopes with different masses. The atomic mass of an element is calculated given the mass and relative abundance of each isotope of the element as it exists in nature. Because the mass of an atom is very small, the mole is used to translate between the atomic and macroscopic levels. A mole is equal to the number of atoms in exactly 12 grams of the isotope carbon-12. The mass of one mole of a substance is equal to its molar mass in grams. The molar mass for a substance can be used in conjunction with Avogadro's number and the density of a substance to convert between mass, moles, volume and number of particles of a sample.

Measurement: SI Units and Conversions

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