2.1 – Data Analysis Objectives: Differentiate between SI base and derived units Identify appropriate SI units for various measurements Convert between common SI prefixes (change magnitudes) Describe the Celsius and Kelvin temperature scales

2.1 – Units of Measurement Systeme International d’Units (SI System) ‘The Metric System’ Uses 7 ‘Base Units’ to measure everything that can be measured Base units reflect some natural constant condition (except kg) Rules of usage An abbreviated metric unit is referred to as a ‘symbol’. Symbols are never followed by a period unless they end a sentence. Symbols should only follow numbers – they’re not abbreviations. Leave a space between the number and the symbol. Symbols are always written in the singular – no ‘s’ to make it plural. Never use ‘p’ in an SI symbol to indicate ‘per’ (as in mph)– use a ‘/’ Capitalization matters – be careful. SI units named after people are not capitalized, but the symbol is.

2.1 – Units of Measurement Systeme International d’Units (SI System) The Base Units Quantity Unit Symbol Length meter m Mass kilogram kg Time second s Electric current ampere A Temperature kelvin K Amount of substance mole mol Luminous intensity candela cd

2.1 – Units of Measurement Systeme International d’Units (SI System) Derived Units Units of measure made by combining the seven base units.

2.1 – Units of Measurement Systeme International d’Units (SI System) Changing Magnitude - Prefixes Prefix Symbol Multiplier giga- G- 1 000 000 000 mega- M- 1 000 000 kilo- k- 1000 hecto- h- 100 deka- da- 10 unit 1 deci- d- 1/10 centi- c- 1/100 milli- m- 1/1000 micro- μ- 1 /1 000 000 nano- n- 1/1 000 000 000 Move the decimal place to the right Move the decimal place to the left

2.1 – Units of Measurement Systeme International d’Units (SI System) Changing Magnitude - Prefixes 0.001 kilo- k- 0.1 deka- da- 0.01 hecto- h- 1.0 unit 10 deci- d- 100 centi- c- 1000 milli- m- King Henry DAngled Under Dirty Capuchin Monkeys King Henry Doesn’t Usually Drink Chocolate Milk

2.1 – Units of Measurement Useful Non-SI Units in Chemistry Liters (L) 1 liter (L) = 1 dm3 1 milliliter (mL) = 1 cm3 1 kiloliter = 1 m3 Celsius (oC) 0 oC = freezing point of pure water at standard pressure 100 oC = boiling point of pure water at standard pressure The Kelvin scale (K) is much better, because there are no negative temperatures, but the Celsius scale is still useful. 0 K = ‘absolute zero’ = -273 oC 0oC = 273 K and 100oC = 373 K Kelvins and oC are the same size, just offset by 273

2.2 – Scientific Notation Objectives: Convert between scientific notation and standard form Use scientific notation correctly with your calculator Solve chemistry calculations using an ordered process Follow units through a calculation Use dimensional analysis to convert between units

2.2 – Scientific Notation Scientific Notation 1 – 9.99 x 10x Used For expressing very large or very small numbers For expressing level of precision (significance) Uses numbers (significant or coefficient) from 1 – 9.99 and a multiplier (exponent) to show order of magnitude. 1 – 9.99 x 10x Positive exponents are used to show values greater than 1. 850 = 8.5 x 10 x 10 = 8.5 x 102 8500. = 8.500 x 10 x 10 x 10 = 8.500 x 103 4321 = 4.321 x 10 x 10 x 10 = 4.321 x 103 2 302 000 = 2.302 x 10 x 10 x 10 x 10 x 10 x 10 = 2.302 x 106 Negative exponents are used to show values less than 1. 0.0023 = 2.3  10  10  10 = 2.3 x 10-3 0.000023 = 2.3  10  10  10  10  10 = 2.3 x 10-5

2.2 – Scientific Notation Scientific Notation 6.02 x 1023 = Samples Put in standard form. 1.87 x 10–5 = 0.0000187 3.7 x 108 = 370 000 000 7.88 x 101 = 78.8 2.164 x 10–2 = 0.02164 Change to scientific notation. 12 340 = 1.234 x 104 0.369 = 3.69 x 10–1 0.008 = 8 x 10–3 1 000 000 000 = 1 x 109 6.02 x 1023 = 602 000 000 000 000 000 000 000

These calculators all show the same number 6.02 x 1023. 2.2 – Scientific Notation Scientific Notation Using your calculator Using scientific notation can cause problems with the order of mathematical operations. Every calculator has a method to enter scientific notation as a single expression so you don’t need ( ). Never use “^”! These calculators all show the same number 6.02 x 1023.

2.2 – Scientific Calculations Chemistry Math Follow the same steps every time!! List the data values given with their correct variable. List the response variable (the variable you are solving for) Select the correct formula. Isolate the response variable Substitute the values and solve. Find the mass of an object with a density of 5 g/mL and a volume of 10 mL. m = ? ρ = 5 g/mL V = 10 mL ρ = m/V (V) ρ = m/V (V) V ρ = m 10 mL  5 g/mL = m 50 g = m

2.2 – Scientific Calculations Chemistry Math Isolating Variables A key step in solving chemistry problems is isolating a variable of interest. The solution of a given equation does not change if we:   Add or subtract the same number from both sides of the equation Solve for x, x + y = z -y + x + y = z – y x = z – y Solve for x, x - y = z +y + x - y = z + y x = z + y

2.2 – Scientific Calculations Chemistry Math Isolating Variables The solution of a given equation does not change if we:   Multiply both the sides with the same number or divide both the sides with the same non-zero number. Solve for x, xy = z xy = z x = z x Solve for x, = z y y y x y = z (y) x y y y = z (y) y x = zy

2.2 – Scientific Calculations Chemistry Math Dealing with Units Units must always be carried through the calculation into the answer: 5.2 kg (2.9 m) (18 s)(1.3 s) = kg•m s2 0.64 4.8 kg (23 s) (18 s)(37 s) = kg s 0.57

2.2 – Data Analysis Dimensional Analysis Converting Units Method of converting units using equivalent measures Conversion factors Any two equivalent measures may be used to write a ratio with a value of 1. This ratio can be used as a conversion factor. 60 min 1 hour = 1 360 min  = 6 hour 1 L 1000 mL = 1 430 mL  = .430 L

2.2 – Data Analysis Dimensional Analysis Converting Units The same unit will always be written diagonally in the expression so that the unit cancels out in the calculation. Write as many conversion factors as necessary to get to answer Example: Convert 2 300 000 seconds into days Multiply across the top, then divide all the way across the bottom Round the answer appropriately 360 min  60 min 1 hour = 6 hour 360 min  1 hour 60 min = 21 600 min2/hr seconds minutes hours days 60 sec 1 min 60 min 1 hour 24 hour 1 day 2 300 000 sec    = 26.62037 days = 27 days

2.2 – Data Analysis Dimensional Analysis The Box Method Method of converting units similar to dimensional analysis using a series of boxes. Place the measurement you are converting from in the top left corner of your boxes. In the next set of boxes, place a ratio that relates your unit to the unit you want to convert to, so that the unit you are converting from cancels out. Example: Convert 2 300 000 seconds into days Multiply across the top, then divide all the way across the bottom Round the answer appropriately 2 300 000 sec 60 sec 1 min 60 min 1 hour 24 hour 1 day = 26.62037 days = 27 days

2.3 – Reliability of Measurements Objectives: Differentiate between accuracy & precision Calculate percent errors for data Identify and use significant digits in calculations

2.3 – Reliability of Measurements Accuracy & Precision Accuracy = comparison of a measure against a known standard If you get the number that is expected when compared to a known standard, the measure is accurate (we calibrate scales to make sure they are accurate) Precision = ability to reproduce the measurement If you can reproduce over and over, the measure is said to be precise If a measure is precise and accurate, then it is said to be reliable.

measured value – accepted value 2.3 – Reliability of Measurements Calculating Percent Error Comparison of a measurement to its accepted value. Percent error is calculated using the formula:   Example: A cookie recipe anticipates a yield of 60 cookies. When the baking is finished only 54 cookies have been produced. Calculate the percent error. measured value = 54 cookies accepted value = 60 cookies * While some people suggest taking the absolute value of this calculation, I prefer using the sign of the calculation. Percent Error = measured value – accepted value x 100 accepted value Percent Error = 54 cookies – 60 cookies x 100 = -10%* 60 cookies

2.3 – Reliability of Measurements Certainty Measurements always include a number of digits that are “certain” and a final digit that is “uncertain”. The final digit is uncertain because: some measuring instruments require estimation some measuring instruments automatically round Require Estimation Automatically Round

2.3 – Reliability of Measurements Making Valid Measurements When using a scaled instrument (ruler, meter stick, graduated cylinder, pipet, buret, etc.) always estimate one place beyond the certainty of the instrument. The human eye is very capable of estimating tenths on most scaled instruments used in the lab. So ALWAYS estimate to the nearest 1/10 of the smallest graduation. 25.45 cm

2.3 – Reliability of Measurements Significant Digits The certain digit(s) plus the final uncertain digit of a measurement are considered “significant”. Rules for identifying sig figs. Non-zero digits are always significant. Zeros between non-zero digits are always significant. Left hand zeroes are never significant. Right hand zeroes are significant when a decimal is present. Counts and defined constants have an infinite number of significant digits. Don’t use them for rounding. 3010 g 1 902.51 g 0.01380 g 0.00103 g 7.123 g 3010 g 1 902.51 g 1.0138 g 0.00103 g 100 033 g 0.301 g 0.0091 g 0.01380 g 0.00103 g 0.6703 g 300.0 g 190 g 12 000 g 12 000. g 0.01030 g

2.3 – Reliability of Measurements Rounding Answers At the end of calculations, the answer must be rounded to the correct number of significant digits. Deciding where to round. In addition and subtraction, round the answer to match the measurement with the fewest decimal places. In multiplication and division, round the answer to match the measurement with the fewest significant digits. 3010 g + 30.6 g = 3040.6 g 3040 g 1 902.51 g + 30.6 g = 1933.11 g 1933.1 g 1.01 g - 0.0306 g = 0.9794 g 0.98 g 13 g - 6 g = 7 g 7 g 3.6 cm x 30.6 cm = 110.16 cm2 110 cm2 2.51 cm x 0.6 cm = 1.506 cm2 2 cm2 1.01 cm3  0.0306 cm = 33.00653 cm2 33.0 cm2 13 cm3  6 cm = 2.166667 cm2 2 cm2

2.3 – Reliability of Measurements Rounding Answers Deciding how to round. After finding the correct rounding position, look at the digits that follow it. If the digits are less than 5, do not change the final digit. If the digits are greater than 5, round the final digit up. If the digits exactly equal 5, round the final digit to be even. 313.251 g  313 g 0.01380 g  0.01 g 313.651 g  314 g 0.01580 g  0.02 g 313.500 g  314 g 0.04500 g  0.04 g

2.4 – Representing Data Objectives: Select appropriate graph types for representing data Determine how different trends appear on graphs Understand why we use best fit lines Calculate slopes for data lines

2.4 – Representing Data Graphing Pie charts Used to represent categorical data as parts of a whole. Pie charts typically depict percentages (fractions). A pie chart is constructed by converting the share of each component part into a percentage of 360o.

2.4 – Representing Data Graphing Bar Graphs Used to represent categorical or numeric values within certain intervals. Bars may be drawn horizontally or vertically. Each bar represents a category, value or range of values. They are often used to show changes over time and clearly illustrate differences in magnitude.

2.4 – Representing Data Graphing Line Graphs Most common graph used in science. They show the relationship between two variables. Line graphs are useful for showing trends. Relationships are typically shown using best-fit lines which may not intersect any of the data points.

2.4 – Representing Data Graphing Trends Reliable data will generally show one of a limited number of trends or relationships: Direct Relationships (Positive Correlation)

2.4 – Representing Data Graphing Trends Inverse Relationships (Negative Correlation)

2.4 – Representing Data Graphing Trends Exponential Relationships Decay Growth

2.4 – Representing Data Best Fit Lines & Slope Best fit lines are used to show the underlying trend of the data in a scatterplot. The trend can then be used to make predictions. Drawing a best fit line simply requires drawing a line through the center of the plotted data so that data points are evenly distributed above and below the line. Making predictions beyond the data points is called extrapolation. Making predictions between the data points is called interpolation.

where ∆ means “change in”. 2.4 – Representing Data Slope The slope of the line may be calculated using the formula slope = ∆y / ∆x where ∆ means “change in”.