Science can be broken into social science (social studies, political science, psychology) and natural science. This slides shows some of the diverse areas of natural science.
Pure science is often what is done at universities and colleges. The basic understanding of why and how things work and react as they do are discovered. The goal in pure science is NOT to make money – but to understand. Industry often funds research at universities in hopes of taking what is learned to make a marketable product and to make money. This synergistic relationship between the business community and academia is beneficial to both parties.
Fleming: biologist knew that bacteria was on everything. Was curious about a moldy orange in his lab. Made a microscope slide and noticed that no bacteria was on the mold. His CURIOSITY helped him to discover penicillin. Charles Martin Hall - was determined to find a method to extract aluminum from the ore bauxite that was readily available in Earth's crust. He succeeded!
Robert Boyle Published The Sceptical Chymist (1661) … stated that scientific speculation was worthless unless it was supported by experimental evidence. This principle led to the development of the scientific method.
Robert Boyle Published The Sceptical Chymist (1661) … stated that scientific speculation was worthless unless it was supported by experimental evidence. This principle led to the development of the scientific method. ROBERT BOYLE: MIGHTY CHEMIST Among the many contenders for the title of &quot; Father of Modern Chemistry &quot; is Robert Boyle (January 25, 1627 - December 30, 1691). Boyle was the first prominent scientist to perform controlled experiments and to publish his work with elaborate details concerning procedure, apparatus and observations. He assembled what we would today call a &quot;research group&quot;, developed a key piece of apparatus - the vacuum pump, was instrumental in founding the Royal Society, and deserves at least partial credit for the famous gas law which bears his name. Boyle was born in Ireland. As the youngest of fourteen children of the wealthiest man in the British Isles, Boyle's opportunities were almost unlimited. However, while still in adolescence, he chose the pseudonym Philaretus (Lover of Truth) and a life of scientific inquiry seemed almost inevitable. He was educated in the finest possible manner of this day, first studying at Eton and later traveling the Continent with a tutor and his older brother Francis. He learned philosophy, religion, languages, mathematics, and - perhaps most significantly - the new physics of Bacon, Descartes, and Galileo. The physical scientists and their new theories concerning air and vacuum, the movement of planets, and the circulation of blood were to sway his thinking much more than the alchemists. Boyle published copiously on topics ranging across several fields of science, philosophy, and theology. His first major scientific report, The Spring and Weight of the Air , was published in 1660 and described experiments using a new vacuum pump of his design. Previous pumps, invented by von Guericke (of Magdeburg hemisphere fame), required the strenuous efforts of two men and provided dubious results. Boyle's pump could be operated easily and efficiently by one man. With it Boyle demonstrated that the sound of a bell in the receiver (a thirty quart vacuum chamber) faded as the air was removed, proving that air was necessary for the transmission of sound. In further experiments, he also proved that air was necessary for life and for a candle flame. Boyle felt that his experiments confirmed a mechanical view of nature as opposed to the Aristotelian, non-empirical approach to science. Today we are so accustomed to empirical science that we have difficulty understanding how one could attempt scientific work using only logic. Boyle's empiricism established him as a founder of the modern scientific method and his arguments were so persuasive as to win many important converts, most notably Isaac Newton. The second edition of The Spring and Weight of the Air , published in 1662, contained the pressure - volume inverse relationship which is familiar to every chemistry student as Boyle's Law . In performing the experiments which led to this generalization, Boyle used mercury in a J-tube and made measurements of the volume of the trapped gas at pressures both higher and lower than normal atmospheric pressure. There is some controversy in naming the relationship after Boyle since much of the work was actually performed by his assistant Robert Hooke, however, the experimental concept originated with Boyle. Furthermore, Boyle was dedicated to the idea of experimental proof of theories while Hooke felt that theories should appeal to reason. Boyle's best known contribution to scientific knowledge is the 1661 publication of The Sceptical Chymist in which he discusses the idea of an element. Aristotelian science held that elements were not just the simplest of all substances but were also necessary ingredients of all bodies, i.e., if water is an element then all bodies must contain at least a small amount of water. Boyle's idea of an element was somewhat vague and certainly not &quot;modern&quot; in the 20th century sense. But he presented persuasive experimental evidence that most of the commonly accepted elements (fire, water, salt, mercury, etc) did not meet both of the Aristotelian criteria. In The Sceptical Chymist , Boyle makes a clear break with the alchemists' tradition of secrecy with his conviction and insistence on publishing in great experimental detail. It is noteworthy that Boyle was among the first to publish the details of his work, including unsuccessful experiments, but Boyle was never able to abandon the beliefs of alchemy. He believed in transmutation of the elements and in 1676, he reported to the Royal Society on his attempts to change quicksilver into gold. He believed that he was near success in this endeavor. In 1654, Boyle had joined a small group of the most influential English scientists, mathematicians, philosophers and physicians who had been meeting weekly in London and in Oxford since 1645. In 1662 the group was chartered as the Royal Society which exists today as the oldest continuous scientific society in the world. The motto of this prestigious organization, &quot;Nullius in Verba&quot; means &quot;nothing in words&quot;, i.e., all science should be experimentally based. In 1680, Robert Boyle was elected president of the Royal Society, but declined the honor because the required oath violated his religious principles. The first use of the term &quot;chemical analysis&quot; is attributed to Boyle who used it in the same sense that we understand it today. He performed assays on gold and silver, tested for copper with ammonia, tested for salt in water with silver nitrate, and devised a thirty item test for mineral water analysis. In addition, he observed that all acids turned a particular vegetable indicator from blue to red and all alkalis turned the indicator green. He found that some substances did not change the color of the indicator and concluded that these were neutral. He thus provided an operational method of classifying substances. Boyle never married and from the age of 41 lived with his sister Katherine, Lady Ranelagh. He was a shy man with deep religious convictions. He had been a pious youth spending some years in the care of the village parson, Mr. W. Douch. Then at the age of 13, during a violent thunderstorm, he experienced a religious conversion not unlike that of St. Paul. Although an ardent defender of the Anglican Church, he was tolerant of the religious views of others and in later years became particularly sympathetic to the Dissenters. He was offered a position in the clergy but felt a stronger commitment to science. He saw no conflict between the two. He wrote widely on religious themes and gave financial support to his his friend Edward Pococke to translate the New Testament into Malayan. He left a large portion of his considerable estate to charitable organizations. Robert Boyle died in London on December 30, 1691. He was buried in the Church of Saint-Martin-in-the-Fields next to his sister. Later the church was demolished and no record was made as to where his remains were moved. Typically, Robert Boyle is remembered solely for Boyle's Law . It is clear that he contributed much more to the development of modern chemical thought. Robert Boyle has been deservedly called &quot;a Mighty Chemist&quot;. Bibliography Dictionary of Scientific Biography , Charles Coulston Gillispie, editor-in-chief, NY Scribner, 1970 D. Thorburn Burns, &quot;Robert Boyle (1627-1691): A Foundation Stone of Analytical Chemistry in the British Isles, Part I. Life and Thought&quot;, Anal. Proc. , 1982 , 19, 222 - 233 D. Thorburn Burns, &quot;Robert Boyle (1627-1691): A Foundation Stone of Analytical Chemistry in the British Isles, Part II. Literary Style, Specific Contributions to the Principles and Practice of Analytical Chemical Science&quot;, Anal. Proc. , 1982 , 19,, 288 - 295 Marie Boas Hall, &quot;Robert Boyle&quot;, Scientific American , 1967 , August, 96 - 102 More, L. T., The Life and Works of the Honourable Robert Boyle , Oxford University Press, London, 1944 http://www.woodrow.org/teachers/chemistry/institutes/1992/Boyle.html
Scientists prefer quantitative data over qualitative data. It is easier to replicate and compare quantitative data.
You can distinguish between a theory and a law by asking the question: Is the proposal measurable? Yes, the statement is a law. No, it is a theory.
Recall, our checkbook activity. Each check represented data. As more data was collected it became clearer what had happened. Some bits of data were unimportant. Most likely, you had to modify your theory as new pieces of data were revealed.
ONLY 3 countries still use the English system of measurement. (England is not one of them!) Myanmar (Burma), Liberia, and United States of America http://upload.wikimedia.org/wikipedia/commons/thumb/1/17/Metric_system.png/800px-Metric_system.png
Internet Access to the National Institute of Standards and Technology “ To be or not to be”: the English or the Metric system The English system of measurement used today in the United States originated in the decrees of English monarchs. The French Revolution produced the overthrow of the French monarchy and in 1799 it also led to the creation of the set of weights and measures we call the metric system. The metric system was legalized for use in the United States in 1866 along with the traditional English system. Today the only countries in the world that do not use the metric system are the United States of America, Liberia and Myanamar. United States government policy toward the Metric System This part is to access the following URLs for the National Institute of Standards and Technology, NIST, and review the evolution of the relationship between the United States and the Metric System. You can answer the first question after reviewing this NIST page. http://ts.nist.gov/ts/htdocs/200/202/ic1136a.htm What was the year when the United States signed the “Treaty of the Meter”? Access this FDA page to answer the following question. http://www.fds.goc/ora/inspect_ref/itg30.html What does the term “Both timeless and toothless” have to do with the Metric Conversions Act of 1975? In your opinion does this influence the pace of metrification in the United States? Name ____________________ Hr ____ Internet Access to the National Institute of Standards and Technology “ To be or not to be”: the English or the Metric system Another part of your assignment is to write a brief argument on the back of this page for adopting the metric system and replacing the English system. Lastly you are to write an argument for continuing the current pattern of using two systems. Argument for adopting the Metric system and dropping the English system. Argument for retaining both the English system and the Metric system
English system of measurement originated in 1215 with the signing of the Magna Carta . It attempted to bring uniform measurements to world trade. In 1790, the French government appointed a committee of scientists to develop a universal measuring system. It took ~10years, and they unveiled the Metric system. length meter m mass gram g volume liter L time second s SI system adopted in 1954. 1 second = time for 9 192 631 770 oscillations of Cs-133 excitation band radiation 1 meter = distance light travels in 1/299 792 458 of a second 1 kilogram = weight of a standard Pt/Ir cylinder (US copy in Gaithersburg); (still artifact-based unit)
Converting between two sets of units never changes the number of significant figures in a measurement. Remember, data are only as good as the original measurement, and no later manipulations can clean them up.
The Scientific Method <ul><li>Mesurements </li></ul><ul><li>Units </li></ul>
Natural Science Physics Chemistry Natural science covers a very broad range of knowledge. Wysession, Frank, Yancopoulos, Physical Science Concepts in Action , 2004, page 4 Physical Science Earth and Space Science Life Science Geology Astronomy Botany Zoology Meteorology Oceanography Ecology Genetics
The Functions of Science pure science applied science the search for knowledge; facts using knowledge in a practical way
Science attempts to establish cause-effect relationships.
Pure Science <ul><li>The search for facts about the natural world. </li></ul>? <ul><ul><li>In science, we often try to establish a cause-effect relationship. </li></ul></ul><ul><ul><li>Driven by curiosity : the need to know, explore, conquer something new. </li></ul></ul>
How does scientific knowledge advance? 1. curiosity 2. good observations 3. determination 4. persistence
Pseudoscience…definitely NOT the Scientific Method
Make observation Ask question Develop hypothesis Test hypothesis with an experiment Analyze data and draw conclusions Hypothesis IS supported Hypothesis is NOT supported Develop theory Test hypothesis with further experiments Revise hypothesis Scientific Method
Using the scientific method requires that one be a good observer. observation inference involves a judgment or assumption uses the five senses
Parts of the Scientific Method <ul><li>Identify an unknown. </li></ul><ul><li>Make a hypothesis </li></ul><ul><li>(a testable prediction). </li></ul><ul><li>Experiment to test the hypothesis. </li></ul><ul><li>Draw a valid conclusion . </li></ul>
The Skeptical Chemist Robert Boyle In “ The Sceptical Chymist” Boyle stated that scientific speculation was worthless unless it was supported by experimental evidence . This principle led to the development of the scientific method . (1661)
Data Observations are also called data . There are two types of data. qualitative data quantitative data descriptions; measurements ; no numbers must have numbers and UNITS
Experiments <ul><li>Law of Nature </li></ul><ul><ul><li>– A verbal or mathematical description of a phenomenon that allows for general predictions </li></ul></ul><ul><ul><li> – Describes what happens and not why </li></ul></ul><ul><ul><li> – Unlikely to change greatly over time unless a major experimental error is discovered </li></ul></ul><ul><ul><li>P·V = P’·V’ Boyle’s Law of gases </li></ul></ul><ul><li>Theory </li></ul><ul><ul><li>– Attempts to explain why nature behaves as it does. </li></ul></ul><ul><ul><li>– Is incomplete and imperfect , evolving with time to explain new facts as they are discovered </li></ul></ul>Copyright 2007 Pearson Benjamin Cummings. All rights reserved.
Scientific Law vs. Scientific Theory Law of Gravity A theory tries to explain why or how something happens. A law states what happens. Theory of Gravity Atomic Theory Collision Theory of Reactions
Scientific Method <ul><li>Observations </li></ul><ul><li>Hypothesis </li></ul><ul><li>Experimentation </li></ul><ul><ul><li>Controlled (one variable changed at a time) </li></ul></ul><ul><ul><li>Collect data (quantitative and qualitative) </li></ul></ul><ul><ul><li>Analyze data (graph, statistics…trends) </li></ul></ul><ul><li>Form valid conclusion. </li></ul><ul><li>After many experiments…form a theory . </li></ul>
Then And Question Research Hypothesis Procedure/ Method Data Observations Conclusion What does the scientist want to learn more about? Gathering of information An “Educated” guess of an answer to the question Written and carefully followed step-by-step experiment designed to test the hypothesis Information collected during the experiment Written description of what was noticed during the experiment Was the hypothesis correct or incorrect? Next Then Next And Finally First Scientific Method An Overview
Measurements Metric (SI) units Prefixes Uncertainty Significant figures Conversion factors Length Density Mass Volume Problem solving with conversion factors Timberlake, Chemistry 7 th Edition, page 40
A physical quantity must include: Number + Unit
The Metric System from Industry Week, 1981 November 30
SI System Map of the world where red represents countries which do not use the metric system
The International System of Units <ul><li>Length meter m </li></ul><ul><li>Mass kilogram kg </li></ul><ul><li>Time second s </li></ul><ul><li>Amount of substance mole mol </li></ul><ul><li>Thermodynamic temperature Kelvin K </li></ul><ul><li>Electric current amperes amps </li></ul><ul><li>Luminous intensity candela cd </li></ul>Quantity Name Symbol Dorin, Demmin, Gabel, Chemistry The Study of Matter , 3 rd Edition, 1990, page 16
The Original Metric Reference (1790) H 2 O = 1 liter Volume 1 kg H 2 O = 1 kilogram Mass 1/10 m 1/10 m 1/10 m = 1 meter Length 1/10,000,000 Earth
The Official Standard Kilogram The Official Standard Meter
Area and Volume: Derived Units Area = length x width = 5.0 m x 3.0 m = 15 ( m x m ) = 15 m 2 Volume = length x width x height = 5.0 m x 3.0 m x 4.0 m = 60 ( m x m x m ) = 60 m 3
Derived Units Commonly Used in Chemistry Area square meter m 2 Volume cubic meter m 3 Force newton N Pressure pascal Pa Energy joule J Power watt W Voltage volt V Frequency hertz Hz Electric charge coulomb C Quantity Name Symbol
Prefixes in the SI System Power of 10 for Prefix Symbol Meaning Scientific Notation _______________________________________________________________________ mega- M 1,000,000 10 6 kilo- k 1,000 10 3 deci- d 0.1 10 -1 centi- c 0.01 10 -2 milli- m 0.001 10 -3 micro- m 0.000001 10 -6 nano- n 0.000000001 10 -9 The Commonly Used Prefixes in the SI System Zumdahl, Zumdahl, DeCoste, World of Chemistry 2002, page 118
Factor Name Symbol Factor Name Symbol 10 -1 decimeter dm 10 1 decameter dam 10 -2 centimeter cm 10 2 hectometer hm 10 -3 millimeter mm 10 3 kilometer km 10 -6 micrometer mm 10 6 megameter Mm 10 -9 nanometer nm 10 9 gigameter Gm 10 -12 picometer pm 10 12 terameter Tm 10 -15 femtometer fm 10 15 petameter Pm 10 -18 attometer am 10 18 exameter Em 10 -21 zeptometer zm 10 21 zettameter Zm 10 -24 yoctometer ym 10 24 yottameter Ym
Significant Figures <ul><li>Indicate precision of a measurement. </li></ul><ul><li>Recording Sig Figs </li></ul><ul><ul><li>Sig figs in a measurement include only the known digits </li></ul></ul>2.3cm
Significant Figures <ul><li>Counting Sig Figs (Table 2-5, p.47) </li></ul><ul><ul><li>Count all numbers EXCEPT: </li></ul></ul><ul><ul><ul><li>Leading zeros – 0,00 25 </li></ul></ul></ul><ul><ul><ul><li>Trailing zeros without a decimal point -- 25 00 </li></ul></ul></ul>
Significant Figures 4. 0,080 3. 5280 2. 402 1. 23.50 Counting Sig Fig Examples 1. 23,50 2. 402 3. 528 0 4. 0,0 80 4 sig figs 3 sig figs 3 sig figs 2 sig figs
Significant Figures <ul><li>Calculating with Sig Figs </li></ul><ul><ul><li>Multiply/Divide - The # with the fewest sig figs determines the # of sig figs in the answer. </li></ul></ul>(13,91g/cm 3 )(23,3cm 3 ) = 324,103g 324 g 4 SF 3 SF 3 SF
Significant Figures <ul><li>Calculating with Sig Figs (con’t) </li></ul><ul><ul><li>Add/Subtract - The # with the lowest decimal value determines the place of the last sig fig in the answer. </li></ul></ul>3.75 mL + 4.1 mL 7.85 mL 224 g + 130 g 354 g 7,9 mL 350 g 3.7 5 mL + 4. 1 mL 7,85 mL 22 4 g + 1 3 0 g 354 g
Significant Figures <ul><li>Calculating with Sig Figs (con’t) </li></ul><ul><ul><li>Exact Numbers do not limit the # of sig figs in the answer. </li></ul></ul><ul><ul><ul><li>Counting numbers: 12 students </li></ul></ul></ul><ul><ul><ul><li>Exact conversions: 1 m = 100 cm </li></ul></ul></ul><ul><ul><ul><li>“ 1” in any conversion: 1 in = 2,54 cm </li></ul></ul></ul>
Significant Figures <ul><li>5. (15,30 g) ÷ (6,4 mL) </li></ul>Practice Problems = 2,390625 g/mL 18.1 g 6. 18,9 g - 0,84 g 18.06 g 4 SF 2 SF 2,4 g/mL 2 SF
Scientific Notation <ul><li>Converting into scientific notation: </li></ul><ul><ul><li>Move decimal until there’s 1 digit to its left. Places moved = exponent. </li></ul></ul><ul><ul><li>Large # (>1) positive exponent Small # (<1) negative exponent </li></ul></ul><ul><ul><li>Only include sig. figs. </li></ul></ul>65000 kg 6.5 × 10 4 kg
Scientific Notation <ul><li>7. 2,400,000 g </li></ul><ul><li>8. 0.00256 kg </li></ul><ul><li>9. 7 10 -5 km </li></ul><ul><li>10. 6.2 10 4 mm </li></ul>Practice Problems 2.4 10 6 g 2.56 10 -3 kg 0.00007 km 62,000 mm
Scientific Notation <ul><li>Calculating with scientific notation </li></ul>(5.44 × 10 7 g) ÷ (8.1 × 10 4 mol) = 5.44 ÷ 7 8.1 4 = 671.6049383 = 670 g/mol = 6.7 × 10 2 g/mol Type on your calculator: EXP EE EXP EE ENTER EXE
Calculation Corner: Unit Conversion 1 min 60 s 60 s 1 min “ Conversion factors” = 180 s 60 s 1 min ( ) 3 min ( )
<ul><li>How many cm are in 1.32 meters? </li></ul>applicable conversion factors: equality: or X cm = 1.32 m = 1 m = 100 cm We use the idea of unit cancellation to decide upon which one of the two conversion factors we choose. (or 0.01 m = 1 cm) ______ 1 m 100 cm ______ 1 m 100 cm ( ) ______ 1 m 100 cm 132 cm
<ul><li>How many meters is 8.72 cm? </li></ul>applicable conversion factors: equality: or X m = 8.72 cm = 1 m = 100 cm Again, the units must cancel. ______ 1 m 100 cm ______ 1 m 100 cm ( ) ______ 0.0872 m 1 m 100 cm
<ul><li>How many feet is 39.37 inches? </li></ul>applicable conversion factors: equality: or X ft = 39.37 in = 1 ft = 12 in Again, the units must cancel. ______ 1 ft 12 in ( ) ____ 3.28 ft 1 ft 12 in ______ 1 ft 12 in
<ul><li>How many kilometers is 15,000 decimeters? </li></ul>X km = 15,000 dm = 1.5 km ( ) ____ 1,000 m 1 km 10 dm 1 m ( ) ______
How many seconds is 4.38 days? = X s = 4.38 d If we are accounting for significant figures, we would change this to… 1 h 60 min 24 h 1 d 1 min 60 s ____ ( ) ( ) ____ ( ) _____ 378,432 s 3.78 x 10 5 s
<ul><li>Measured dimensions of a rectangle: </li></ul>Find area of rectangle. A = L . W = (9.70 cm)(4.25 cm) length (L) = 9.70 cm width (W) = 4.25 cm = Example Problem 41.2 cm 2 . cm L W
<ul><li>Convert 41.2 cm 2 to m 2 . </li></ul>X m 2 = 41.2 cm 2 X m 2 = 41.2 cm . cm Recall that… 41.2 cm 2 = 41.2 cm . cm X m 2 = 41.2 cm 2 = 0.412 m 2 = 0.412 cm . m WRONG! = 0.00412 m 2 = 0.00412 m 2 100 cm 1 m ( ) ______ 100 cm 1 m ( ) ______ ( ) ______ 100 cm 1 m ( ) ______ 100 cm 1 m 2
<ul><li>Convert 41.2 cm 2 to mm 2 . </li></ul>X mm 2 = 41.2 cm 2 X mm 2 = 41.2 cm . cm Recall that… 41.2 cm 2 = 41.2 cm . cm = 4,120 mm 2 = 4,120 mm 2 1 cm 10 mm ( ) _____ 1 cm 10 mm ( ) _____ 1 cm 10 mm 2 ( ) _____
<ul><li>Measured dimensions of a rectangular solid: </li></ul>Find volume of solid. L W H Length = 15.2 cm Width = 3.7 cm Height = 8.6 cm V = L . W . H = (15.2 cm)(3.7 cm)(8.6 cm) = 480 cm 3
<ul><li>Convert to m 3 . </li></ul>X m 3 = 480 cm 3 = 0.000480 m 3 3 X m 3 = 480 cm 3 = X m 3 = 480 = or cm . cm . cm 4.80 x 10 -4 m 3 or 3 2 cm 100 cm 1 m ( ) _____ 100 cm 1 m ( ) _____ 100 cm 1 m ( ) _____ 100 cm 1 m ( ) _____ 1 m 1000000 cm ( ) _________ 3 3
<ul><li>Measured dimensions of a rectangular solid: </li></ul>Find volume of solid. L W H Length = 15.2 cm Width = 3.7 cm Height = 8.6 cm V = L . W . H = (0.152 m)(0.037 m)(0.086 m) = 0.000480 m 3 0.152 m 0.037 m 0.086 m Convert to m 3 ...
<ul><li>Direct Proportion </li></ul><ul><li>Inverse Proportion </li></ul>Proportions: GRAPHICS y x y x
Rules for Counting Significant Figures 1. Nonzero integers always count as significant figures. 2. Zeros: There are three classes of zeroes. <ul><li>Leading zeroes precede all the nonzero digits and DO NOT count as </li></ul><ul><li>significant figures. Example: 0.0025 has ____ significant figures. </li></ul><ul><li>Captive zeroes are zeroes between nonzero numbers. These always </li></ul><ul><li>count as significant figures. Example: 1.008 has ____ significant figures. </li></ul><ul><li>Trailing zeroes are zeroes at the right end of the number. </li></ul><ul><li>Trailing zeroes are only significant if the number contains a decimal point. </li></ul><ul><li>Example: 1.00 x 10 2 has ____ significant figures. </li></ul><ul><li>Trailing zeroes are not significant if the number does not contain a decimal </li></ul><ul><li>point. Example: 100 has ____ significant figure. </li></ul><ul><li>Exact numbers, which can arise from counting or definitions such as 1 in </li></ul><ul><li> = 2.54 cm, never limit the number of significant figures in a calculation. </li></ul>2 4 3 1
Significant figures: Rules for zeros Leading zeros are not significant. Captive zeros are significant. Trailing zeros are significant. Leading zero Captive zero Trailing zero 0.421 4012 114.20 – three significant figures – four significant figures – five significant figures
Significant Figures Number of Quantity Certain Digits Significant Figures 14.37 9 g 1 4 3 7 9 9 (thousandths) 5 6.0 2 mL 6 0 2 2 (hundredths) 3 120.58 0 m 1 2 0 5 8 0 0 (thousandths) 6 7. 5 g 7 5 5 (tenths) 2 0.03 7 g 3 7 7 (thousandths) 2 0.037 0 g 3 7 0 0 (ten-thousandths) 3 *The position of the decimal point has nothing to do with the number of significant figures.