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Why would we use scientific notation?

REALLY, REALLY SMALL NUMBERS. SCIENTIFIC NOTATION A QUICK WAY TO WRITE REALLY, REALLY BIG OR REALLY, REALLY SMALL NUMBERS.

Rules for Scientific Notation To be in proper scientific notation the number must be written with * a number between 1 and 10 * and multiplied by a power of ten 23 X 105 is not in proper scientific notation. Why?

0.0000187 370,000,000 78.8 0.02164 Change to standard form. 1.87 x 10–5 = 3.7 x 108 = 7.88 x 101 = 2.164 x 10–2 = 0.0000187 370,000,000 78.8 0.02164

Change to scientific notation. 12,340 = 0.369 = 0.008 = 1,000. = 1.234 x 104 3.69 x 10–1 8 x 10–3 1.000 x 103

SI System The International System of Units Derived Units Commonly Used in Chemistry 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 Map of the world where red represents countries which do not use the metric system

The International System of Units Quantity Name Symbol Length meter m Mass kilogram kg Time second s Amount of substance mole mol Temperature Kelvin K Electric current amperes amps Luminous intensity candela cd 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 ____ 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 Dorin, Demmin, Gabel, Chemistry The Study of Matter , 3rd Edition, 1990, page 16

NEED TO KNOW Prefixes in the SI System Power of 10 for Prefix Symbol Meaning Scientific Notation _________________________________________________________ mega- M 1,000,000 106 kilo- k 1,000 103 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

Significant figures ??? Method used to express accuracy and precision. You can’t report numbers better than the method used to measure them. 67.20 cm = four significant figures ??? Certain Digits Uncertain Digit

The number of significant digits is independent of the decimal point. Significant figures The number of significant digits is independent of the decimal point. 255 31.7 5.60 0.934 0.0150 These numbers All have three significant figures!

Rules for Counting Significant figures Every non-zero digit is ALWAYS significant! Zeros are what will give you a headache! They are used/misused all of the time.

Rules for zeros Leading zeros are not significant. ??? Captive zeros are always significant! 0.421 - three significant figures Leading zero ??? 4,008 - four significant figures Captive zeros ??? Trailing zeros are significant … IF there’s a decimal point in the number! 114.20 - five significant figures Trailing zero ???

Examples 250 mg \__ 2 significant figures 120. miles 0.00230 kg 23,600.01 s \__ 7 significant figures

Significant figures: Rules for zeros Scientific notation - can be used to clearly express significant figures. A properly written number in scientific notation always has the proper number of significant figures. 0.00321 = 3.21 x 10-3 Three Significant Figures

Significant figures and calculations An answer can’t have more significant figures than the quantities used to produce it. Example How fast did you run if you went 1.0 km in 3.0 minutes? 0.333333 speed = 1.0 km 3.0 min = 0.33 km min

Significant figures and calculations Multiplication and division. Your answer should have the same number of sig figs as the original number with the smallest number of significant figures. ONLY 3 SIG FIGS! 21.4 cm x 3.095768 cm = 66.2 cm2 135 km ÷ 2.0 hr = 68 km/hr ONLY 2 SIG FIGS!

Significant figures and calculations Addition and subtraction Your answer should have the same number of digits to the right of the decimal point as the number having the fewest to start with. 123.45987 g + 234.11 g 357.57 g 805.4 g - 721.67912 g 83.7 g

Rounding off numbers After calculations, you may need to round off. If the first insignificant digit is 5 or more, you round up If the first insignificant digit is 4 or less, you round down.

Examples of rounding off If a set of calculations gave you the following numbers and you knew each was supposed to have four significant figures then - 2.5795035 becomes 2.580 34.204221 becomes 34.20 1st insignificant digit

Examples of Rounding For example you want a 4 Sig Fig number 0 is dropped, it is <5 8 is dropped, it is >5; Note you must include the 0’s 5 is dropped it is = 5; note you need a 4 Sig Fig 4965.03   780,582 1999.5 4965 780,600 2000.

Multiplication and division 32.27  1.54 = 3.68  .07925 = 1.750  .0342000 = 3.2650106  4.858 = 6.0221023  1.66110-24 = 49.6958 46.4353312 0.05985 1.586137 107 1.000000 49.7 46.4 0.05985 1.586 107 1.000