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Why do we need it? Because in chemistry we are measuring very small things like protons and electrons and we need an easy way to express these numbers. Scientific notation expresses numbers as a multiple of two factors: 1)A number between 1 and 10. 2)Ten is raised to an exponent and this tells you how many times the factor should be multiplied by ten. SCIENTIFIC NOTATION

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To express a number in scientific notation move the decimal point until after the first digit and count the positions you moved it. If you move it to the left, you are making the number smaller, so to keep the same number, multiply it by 10 elevated to the positive power of the positions moved. 3,591 = 3.591 X 10 3 3,591 SCIENTIFIC NOTATION

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If you move it to the right, you are making the number bigger, so to keep the same number, multiply it by 10 elevated to the negative power of the positions moved. 0.0000345= 0.0000345 3.45 X10 -5 SCIENTIFIC NOTATION

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Summarizing… If the number is LARGER than 1 the exponent of 10 is POSITIVE. If the number is SMALLER than 1 the exponent of 10 is NEGATIVE.

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Practice: 1,222,000,000 = 0.00002035 = 0.9999 = 109 = 100,000 = 1.222 x 10 9 2.035 x 10 -5 9.999 x 10 -1 1.09 x 10 2 1 x 10 5 Convert to scientific notation

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More Practice: 25,000,000 = 0.012 = 0.00000001 = 345.9 = 45.803 x 10 -5 = 2.5 x 10 7 1.2 x 10 -2 1 x 10 -8 3.459 x 10 2 4.5803 x 10 -4

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More Practice: 1.14 x 10 4 = 9.08 x 10 -4 = 1.112 x 10 6 = 2.32 x 10 -9 = 5.83 x 10 -5 = 11,400 0.000908 1,112,000 0.00000000232 0.0000583 Convert these to numbers not in scientific notation

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Multiplication: 1) Multiply the factors 2) Add the exponents. Multiplications and divisions with exponential numbers Example: 2.3 X 10 3 X 2.0 X 10 2 = 1.5 X 10 -6 X 3.0 X 10 4 = 2.1 X 10 -3 X 4.0 X 10 -2 = 4.6 X 4.5 X 8.4 X 10 5 10 -2 10 -5

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1) Divide the factors 2) Subtract the exponents (numerator – denominator). Division Example: 2.4 X 10 3 = 2.0 X 10 2 6.3 X 10 -4 = 3.0 X 10 2 8.4 X 10 3 = 4.0 X 10 -2 1.2 X 2.1 X 10 10 -6 10 5

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Practice: 1) 3.4 X 10 4 = 2.1 X 10 2 2) 4.3 X 10 5 X 8.0 X 10 3 = 3) 9.8 X 10 -5 = 7.3 X 10 2 4) 6.9 X 10 -2 X 2.4 X 10 3 = 5) 2.3 X 10 -5 X 5.0 X 10 -3 = 6) 1.7 X 10 -5 = 1.4 X 10 -6 1.6 x 10 2 3.4 x 10 9 1.2 x 10 1.2 x 10 -7 1.7 x 10 2 1.3 x 10 -7

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Adding and Subtracting in Scientific Notation You must be sure that the exponents are the SAME. Then when you add the non-exponential numbers the exponents stay the same. Example:

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Base Units In science we use _________ which are numbers with __________, because the number alone doesn’t tell you the value of the measurement. For example if I measure the length of an object, if I say it is 3.0, it could be as short as 3.0 mm or as long as 3.0 Km therefore I must specify the unit used to compare it. quantities units

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…cont…Base Units Standard units of measurements are necessary because scientists need to report data that others scientists can__________, therefore they use the _____ system (Systeme Internationale d’Unites), International System. A defined unit in a system of measurement is called _______ unit. It is based on an object or event in the physical world. reproduce SI base

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SI Base Units QuantityBase UnitAbbreviation Length Time Mass Temperature Amount of a substance Luminous intensity Electric current meterm seconds kilogram Kg kelvin K mole mol candelacd ampere A

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Definitions of some derived units The __second___ is the frequency of microwave given of by a Cesium-13 atom. The ___meter ___ is the distance that light travels through __vacuum__ in 1/299,792,485 of a second. The __Kilogram___ is the mass of a platinum iridium cylinder metal stored in a triple bell jar, in Sevres, Paris. A __derived unit__ is a unit defined by a combination of base units. Examples : m/s, Km/h.

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Derived units The volume expressed in cm 3 and dm 3 is a derived unit. 1 dm 3 = __1__ L 1 cm 3 = __1_ mL 1 L = _1,000 mL 1 dm 3 = _1,000 cm 3 A derived unit that relates the mass of an object per unit of volume is __density_.

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Derived units The density of a substance is obtained dividing the _______ by the ________ of the object. Density can be measured in __g/cm 3, g cm -3 __ or __g/mL__ Calculate the density of an object with a mass of 3.50g and which cause the water in a graduated cylinder to change from 12.5 mL to 18.7 mL. massvolume

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Temperature The three scales for temperature are the ___Celsius___, __Fahrenheit and __Kelvin__. To change °C to °F the formula is: __°F =__9/5°C + 32 º To change °F to °C the formula is: °C =_5/9( o F- 32 o ) Examples: Convert the following temperature to Fahrenheit a) 25.0 o C b) 32.0 o C c) -7.8 o C Convert the following temperature to Celsius d) 70.0 o F e) 120.0 o F f) 50.0 o F

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Temperature To change °C to K the formula is: K_=_ o C + 273.16 To change K to °C the formula is: °C =__K – 273.16_ Examples: Convert the following temperatures to K a)25.00 o C b) 32.43 o C c) -7.81 o C Convert the following temperatures to Celsius d) 300.00K e) 298.16K f) 79.38K

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Complete the following table CelsiusFahrenhe it Kelvin Freezing point of water Boiling point of water Absolute zero 0 Room temperature 24 0

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Conversion factors A conversion factor is a ratio of equivalent values used to express the same quantity in different units. A conversion factor is always equal to 1 Dimensional Analysis uses __________________________. Look at the table of prefixes Observe the values and the meanings Complete the meanings

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Practice: Express 2.45 x 10 2 hg in : a) g b) g and c) Eg Solution a: Write the given with the unit : 2.45 x 10 2 hg Multiply by a ratio x Write the unit that you want to cancel in the denominator hg Put the unit that you want to obtain in the numerator gg Put the values to the fraction that will make numerator and denominator equivalent 1 10 8 Cancel out the equivalent units in the numerator and denominator Multiply the quantity by the numerator and divide by the denominator = 2.45 x 10 10 g

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3.5 x 10 3 g x CONVERSIONS g mg 1 10 3 = 3.5 x 10 6 mg Express 3.5 x 10 3 g in : a) mg b) Pg and c) Kg 3.5 x 10 3 g x g Pg 1 10 15 = 3.5 x 10 -12 Pg 3.5 x 10 3 g x g Kg1 10 3 = 3.5 Kg

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More practice: Express 1)5.1 Kg in a) pgb) gc) Mg 2) 4.0 x 10 –7 Gm in a) Tm b) m c) am 3) 27 Kg in a) ngb) gc) Mg 4) 1.67 x 10 2 Gm in a) Tm b) m c) am

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NumberDigits to Count as Significant Examples# of Significant Digits Nonzero digits All3,279 239 Leading zeroes Leading zeroes (zeroes before integer) None0.0045 0.00001 Captive zeroes Captive zeroes (zeroes between two integers) All5.007 205 Trailing zeroes Trailing zeroes (zeroes after the last integer) Counted only if the number contains a decimal point 100 100. 100.0 0.0100 Scientific notationAll in non- exponential part 1.7x10 -7 1.30x10 2 3 4 3 2 1 4 3 1 3 4 3 (1 and 0’s following 1) 2 3

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Uncertainty, accuracy and precision The last digit recorded in any measurement is an estimate and therefore it is UNCERTAIN. 6.52 6.53 6.54 The 6 and the 5 are certain.The red digits is uncertain. A measurement must be recorded with all the certain digits and only one uncertain.

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Let’s compare The mass of an object measured in a simple balance was: The mass of the same object measured in the analytical balance was: 2.359 are certain digits (you know them for sure). The last 6 is the estimate. 2.36g The 2 and the 3 are certain digits But the 6 is uncertain. So you know for sure 2.3, but the following digit could be 5,6, 7 or even 4 or 9 because it is an estimate. 2.3596g Which balance is more precise?

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Accuracy: How close the number is to the accepted value. Precision: How close the values are to each other. The smaller the uncertainty the greater the precision.

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The accuracy of a measurement depends on the calibration of the tool and also on how carfully the experimenter do the measurements. Well calibrated tools should give more accurate measurements if they are carefully done. The precision depends on the tool. The analytical balance allows you to read more decimals and that is why it is more precise.

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More precise tools should give more accurate values, but that is not always the case. For example: The boiling point of water is 100 0 C (Accepted value) Three thermometers were used to measure it experimentally. 100.00 o C 100. o C 101.445 o C Classify each of them as accurate, precise or both

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Random error: A measurement has equal possibilities of being high or low. Systematic error: measurements are either all high or all low. Example of Random error: In a certain experiment the values obtained for the boiling point of water Were: 100.0 o C, 99.8 o C, 100.3 o C, 100.2 o C, 99.9 o C How do you solve it? Getting the average of the values Example of systematic error: In another experiment the values obtained for the boiling point of water were: 100.2 o C,100.8 o C, 100.3 o C, 100.2 o C, 100.9 o C How do you solve it? Calibrating the tool used to do the measurements

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Significant figures or significant digits of a measurement are all the certain digits plus one and only one uncertain. When multiplying and/or dividing : Count the number of significant digits in each measurement. Significant figures in calculations Report the answer with the same amount of significant digits as the measurement with the least amount of significant digits. Remember that exact numbers have infinite amount of significant figures. 3.802 x 2.0 = Only 2 significant figures Answer: 7.6 4 significant figures 2 significant figures

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Count the decimals in each measurement. Uncertainty in additions and subtractions Report the answer with the same amount of decimals as the measurement with the least amount of decimals. Remember the rules for rounding when doing your calculations. Example. 2.038 + 2.1 3 decimals 1 decimal 2.038 + 2.1 = 4.1 (1 decimal)

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