1 What is the Length? We can see the markings between cm We can’t see the markings between the.6-.7 We must guess between.6 &.7 We record 1.67 cm as our measurement The last digit an 7 was our guess...stop there

Learning Check What is the length of the wooden stick? 1) 4.5 cm 2) 4.58 cm 3) cm

Measurement and Significant Figures Every experimental measurement has a degree of uncertainty. The volume, V, at right is certain in the 10’s place, 10mL<V<20mL The 1’s digit is also certain, 17mL<V<18mL A best guess is needed for the tenths place. Chapter Two 3

Scientific Notation Find your Notecard Partner. Why would we use scientific notation?

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

Scientific Notation # from 1 to x 10 exponent 800= 8 x 10 x 10 = 8 x = x 10 x 10 x 10 = x = 1.4 ÷ 10 ÷ 10 ÷ 10 = 1.4 x 10 -3

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 10 5 is not in proper scientific notation. Why?

Change to standard form x 10 –5 = 3.7 x 10 8 = 7.88 x 10 1 = x 10 –2 = 370,000,

Change to scientific notation. 12,340 = = = 1,000. = x x 10 –1 8 x 10 – x 10 3

The International System of Units Lengthmeter m Masskilogram kg Timesecond s Amount of substancemole mol TemperatureKelvin K Electric currentamperes amps Luminous intensitycandela cd QuantityNameSymbol Dorin, Demmin, Gabel, Chemistry The Study of Matter, 3 rd Edition, 1990, page 16

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

NEED TO KNOW Prefixes in the SI System Power of 10 for Prefix SymbolMeaning Scientific Notation _________________________________________________________ mega-M 1,000, kilo-k 1, deci-d centi-c milli-m micro-  nano-n pico-p

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

Significant figures The number of significant digits is independent of the decimal point 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. SEE p.24 in your book!

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

Examples 250 mg \__ 2 significant figures 120. miles \__ 3 significant figures kg \__ 3 significant figures 23, s \__ 7 significant figures

Significant figures: Rules for zeros Scientific notation 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 = 3.21 x Three Significant Figures 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? 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 cm x cm = 66.2 cm km ÷ 2.0 hr = 68 km/hr ONLY 3 SIG FIGS! 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 g g g g 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.

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

Examples of Rounding For example you want a 4 Sig Fig number , 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 ,

Multiplication and division  1.54 =  =  =  10 6  =     = 