Analyzing Data Chapter 2

Units & Measurement – section 1 Chemists use an internationally recognized system of units to communicate their findings.

SI Units of Measure All measurements need a number and a ______________. Example: 5 ft 3 in or 25ºF Scientists usually do not use these units. They use a unit of measure called SI or _____________________________________________. Base Units – more examples on following slide ________ - straight line distance between 2 points is the meter (m) _________ -quantity of matter in an object or sample is the kilogram (kg)

The International System of Units

SI Units of Measure Derived Units These are units that are made from ________________ of base units. _____________ -amount of space taken up by an object. l x w x h (m3) ____________ -ratio of an object’s mass to its volume. D = m/v (kg/m3)

SI Unit of Measure

Metric Prefixes 0.009 seconds = 9 milliseconds (ms) 12 km = 12000 meters Gigabyte = 1,000,000,000 bytes Megapixel = 1,000,000 pixels Some common prefixes: _______ - 1000 Hecta- 100 ________ - 10 (base unit) 1 _________ - 0.1 Centi- 0.01 _________ - 0.001 Nutrition labels often have some measurements listed in grams and milligrams

Measuring Temperature ______________ An instrument that measures temperature, or how hot an object is. Fahrenheit scale: water freezes at 32ºF and boils at 212 ºF  Celsius scale: water freezes at _____ and boils at ______ºC  ºC = 5 (ºF- 32) ºF = 9 ºC + 32 9 5   The SI unit for temperature is the _____________(K) 0K is the lowest possible temperature that can be reached. In ºC, it is -273.15 ºC K = ºC + 273 ºC = K – 273

Conversion Factors Conversion Factors- Ratio of equivalent measurements that is used to convert a quantity expressed in one unit to another ____________. Examples: 1 km or 1000 m 1000 m 1 km 1000 m = 100 Dm = 10 hm = 1 km

Primary conversion factor: 8848m ( 1km ) = 8.848 km 1000m Secondary conversion factor: 12 km (1000m) (1000mm) = 1.2 x 107 mm or 12,000,000 mm 1km 1m  Tertiary conversion factor: 5 km (1000m) ( 1hr ) = 1.39 m/sec 1 hr 1 km 3600sec

REVIEW Units & Measurement What are the SI base units for time, length, mass, and temperature? How does adding a prefix change a unit? How are the derived units different for volume and density?

REVIEW Units & Measurement - Vocab Base unit – Second – Meter – Kilogram – Kelvin – Derived unit – Liter – Density -

Scientific Notation – section 2 Scientists use scientific methods to systematically pose and test solutions to questions and assess the results of the tests.

Scientific Notation _________Notation – They way we are use to seeing numbers. Example: Three hundred million = 300,000,000 __________Notation – A way of expressing a value as the product of a number between 1 and 10 and a power of 10. 300,000,000 = 3.0 x 108 The exponent 8 tells you the decimal point is really eight places to the right of 3. 0.00086 = 8.6 x 10-4 The exponent -4 tells you the decimal point is really four places to the left of 8 Scientists estimate that there are more than 200 billion stars in the Milky Way galaxy.

Scientific Notation Adding & subtracting Multiplying & dividing To add and subtract numbers they MUST have the same ________, if they do not you need to write in standard notation and then put back to scientific notation Example: 8.6 x 10-4 + 6 x 10-4 & 8.6 x 10-4 + 6 x 10-5 Multiplying & dividing To multiply, 1st multiple the coefficients then _____the exponents. Example: 8 x 10-4 X 6 x 10-4 To divide, 1st divide the coefficients then ________the exponents. Example: 8 x 10-4 / 6 x 10-5

Math Practice Perform the following calculations. Express your answers in scientific notation. (7.6 × 10−4 m) × (1.5 × 107 m) 0.00053 ÷ 29 2.Calculate how far light travels in 8.64 × 104 seconds. (Hint: The speed of light is about 3.0 × 108 m/s.)1.Perform the following calculations. Express your answers in scientific notation.

REVIEW Scientific Notation Why use scientific notation to express numbers? How is dimensional analysis used for unit conversion?

REVIEW Scientific Notation - Vocab

Uncertainty & Representing Data – section 3 & 4 Measurements contain uncertainties that affect how a calculated result is presented. Graphs visually depict data, making it easier to see patterns and trends.

Limits of Measurement _____________A gauge of how exact a measurement is Significant figures- all the digits that are known in a measurement, plus the last digit is estimated. 5.25 minutes has 3 significant figures. 5 minutes has 1 significant figure. The fewer the significant figures, the less precise the measurement is. The precision of a calculated answer is limited by the least precise measurement used in the calculation. Example: Density = 34.73g = 7.857466 g/cm3 4.42cm3 You must round to 3 significant figures: 7.86 g/cm3

________Closeness of a measurement to the actual value of what is being measured. Example: A clock running fast will be precise to the nearest second, but it won’t be accurate, or close to the correct time. A more precise time can be read from the digital clock than can be read from the analog clock. The digital clock is precise to the nearest second, while the analog clock is precise to the nearest minute.

Accuracy vs Precision Accuracy refers to how close a measured value is to an accepted value. Precision refers to how close a series of measurements are to one another.

Error _____________is defined as the difference between an experimental value and an accepted value. a: These trial values are the most precise b: This average is the most accurate

% Error The error equation is error = experimental value – accepted value. ________________ expresses error as a percentage of the accepted value. Example: You conducted an experiment and concluded that 84 pineapples would ripen but only 67 did. What was your % error?

Significant Figures Often, precision is limited by the tools available. Significant figures include all known digits plus one estimated digit.

Sig Fig Rules Significant Figures Rules for significant figures: Rule 1: _________________numbers are always significant. Rule 2: __________between nonzero numbers are always significant. Rule 3: All final zeros to the right of the decimal are significant. Rule 4: Placeholder zeros are not significant. To remove placeholder zeros, rewrite the number in scientific notation. Rule 5: Counting numbers and defined constants have an ________number of significant figures.

Sig Fig Practice

Rounding Rounding Numbers Calculators are not aware of significant figures. Answers should not have more significant figures than the original data with the fewest figures, and should be rounded. Rules for rounding: Rule 1: If the digit to the right of the last significant figure is less than 5, do not change the last significant figure. 2.532 → 2.53 Rule 2: If the digit to the right of the last significant figure is greater than 5, round up the last significant figure. 2.536 → 2.54 Rule 3: If the digits to the right of the last significant figure are a 5 followed by a nonzero digit, round up the last significant figure. 2.5351 → 2.54 Rule 4: If the digits to the right of the last significant figure are a 5 followed by a 0 or no other number at all, look at the last significant figure. If it is odd, round it up; if it is even, do not round up. 2.5350 → 2.54 2.5250 → 2.52

Rounding Rounding Numbers ______________________________________ Round the answer to the same number of decimal places as the original measurement with the fewest decimal places. ____________________________________ Round the answer to the same number of significant figures as the original measurement with the fewest significant figures.

Scientists can organize their data by using data tables and graphs Organizing Data Scientists can organize their data by using data tables and graphs Data table- the simplest way to organize data. The table shows two variables - a ______________variable and the ________________variable. 

Line graph Line graphs are useful for showing changes that occur in related variables. It shows the manipulated variable on the x-axis and the responding variable on the y-axis. Slope- (steepness) The ratio of a vertical change to the corresponding horizontal change. Slope = Rise Run Rise represents the change in the _______________________ Run represents the corresponding change in the ____________________

________proportion- Relationship in which the ratio of the two variables is constant. ________proportion- Relationship in which the product of the two variables is constant.

______ graphs and ______ or circle graphs can also be used to display data.

REVIEW Uncertainty & Representing Data How do accuracy and precision compare? How can the accuracy of data be described using error and percent error? What are the rules for significant figures and how can they be used to express uncertainty in measured and calculated values? Why are graphs created? How can graphs be interpreted?

REVIEW Uncertainty & Representing Data - Vocab Accuracy – Precision – Error – percent error – significant figure – Graph -