Uncertainty in Measurement A digit that must be estimated is called uncertain. A measurement always has some degree of uncertainty.

Precision and Accuracy Accuracy refers to the agreement of a particular value with the true value. Precision refers to the degree of agreement among several measurements made in the same manner. Neither accurate nor precise Precise but not accurate Precise AND accurate

Types of Error Random Error (Indeterminate Error) - measurement has an equal probability of being high or low. Systematic Error (Determinate Error) - Occurs in the same direction each time (high or low), often resulting from poor technique or incorrect calibration.

Why Is there Uncertainty?  Measurements are performed with instruments  No instrument can read to an infinite number of decimal places Which of these balances has the greatest uncertainty in measurement?

Rules for Counting Significant Figures - Details Nonzero integers always count as significant figures has 4 sig figs.

Rules for Counting Significant Figures - Details Zeros - Leading zeros do not count as significant figures has 3 sig figs.

Rules for Counting Significant Figures - Details Zeros - Captive zeros always count as significant figures has 4 sig figs.

Rules for Counting Significant Figures - Details Zeros Trailing zeros are significant only if the number contains a decimal point has 4 sig figs.

Rules for Counting Significant Figures - Details Exact numbers have an infinite number of significant figures. 1 inch = 2.54 cm, exactly

Atlantic Pacific Rule Atlantic Pacific Rule 1. If decimal is Present, count from the Pacific starting with the first nonzero digit. 2. If decimal is Absent, count from the Atlantic starting with the first non zero digit.

PacificAtlantic (Decimal present)(Decimal absent) 1) )765,300 1)3 2)4

Sig Fig Practice #1 How many significant figures in each of the following? m  5 sig figs kg  4 sig figs 100,890 L  5 sig figs 3.29 x 10 3 s  3 sig figs cm  2 sig figs 3,200,000  2 sig figs

Rules for Significant Figures in Mathematical Operations Multiplication and Division: # sig figs in the result equals the number in the least precise measurement used in the calculation x 2.0 =  13 (2 sig figs)

Sig Fig Practice # m x 7.0 m CalculationCalculator says:Answer m 2 23 m g ÷ 23.7 cm g/cm g/cm cm x cm cm cm m ÷ 3.0 s m/s240 m/s lb x 3.23 ft lb·ft 5870 lb·ft g ÷ 2.87 mL g/mL2.96 g/mL

Rules for Significant Figures in Mathematical Operations Addition and Subtraction: The number of decimal places in the result equals the number of decimal places in the least precise measurement =  18.7 (3 sig figs)

Sig Fig Practice # m m CalculationCalculator says:Answer m 10.2 m g g g 76.3 g 0.02 cm cm cm 2.39 cm L L L709.2 L lb lb lb lb mL mL 0.16 mL mL

Outcomes Over the Long-Term Theory (Model) - A set of tested hypotheses that give an overall explanation of some natural phenomenon. overall explanation of some natural phenomenon. Natural Law - The same observation applies to many different systems different systems - Example - Law of Conservation of Mass

Law vs. Theory A law summarizes what happens  A law summarizes what happens  A theory (model) is an attempt to explain why it happens.

Nature of Measurement Part 1 - number Part 2 - scale (unit) Examples: 20 grams 6.63 x Joule seconds Measurement - quantitative observation consisting of 2 parts consisting of 2 parts

Steps in the Scientific Method 1.Observations - quantitative - qualitative 2.Formulating hypotheses - possible explanation for the observation 3.Performing experiments - gathering new information to decide whether the hypothesis is valid whether the hypothesis is valid

The Fundamental SI Units (le Système International, SI)

SI Prefixes Common to Chemistry PrefixUnit Abbr.Exponent Kilok10 3 Decid10 -1 Centic10 -2 Millim10 -3 Micro  10 -6

Derived SI Units Derived-combo of standard base units produced by either multiplying of dividing. Quantitysymbolunit abbrev. Derivation AreaAm² length x width VolumeVm³l x w x h DensityDkg/m³mass/volume

Volume- amount space occupied by an object *units used in the laboratory 1m³= 1,ooo,ooocm³ L= 1000cm³ 1000mL= 1L 1000cm³= 1000mL *cm³ and mL are interchangeable

Density- ratio of mass to volume Density = Mass Volume base unit mass=kg base unit volume=m³ kg/m³g/cm³g/mL DV M

Calculate 1. What is the density of a block of marble that occupies 310cm³ and has a mass of 853g? Answer-2.8 g/cm³

2. Diamond has a density of 3.26g/cm³. what is the mass of a diamond that has a volume of 0.35cm³? Answer-1.1 g

Conversion Factors A ratio derived from the equality between two different units that can be used to convert from one unit to the other.

4 quarters=11 dollar=10.25 dollar=1 1 dollar4quaters1 quarter *Quantity sought=quantity given x conversion factor

How many quarters are in twelve dollars? # of quarters = 12 dollars x conversion factor ? Quarters = 12 dollars4 quarters 1 dollar = 48 quarters

What is the price of a piece of copper Wire 325cm long that sells for $.15/ft? 1 in = 2.54cm