Analyzing Data Chapter 2

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

BNTSG overview of metric 

SI Units of Measure  All measurements need a number and a unit.  Example: 5 ft 3 in or 25ºF  Scientists usually do not use these units. They use a unit of measure called SI or International System of Units.  Base Units – more examples on following slide  Length- straight line distance between 2 points is the meter (m)  Mass- 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 combinations of base units.  Volume- amount of space taken up by an object. l x w x h (m 3 )  Density- ratio of an object’s mass to its volume. D = m/v (kg/m 3 )

SI Unit of Measure

Metric Prefixes  seconds = 9 milliseconds (ms)  12 km = meters  Gigabyte = 1,000,000,000 bytes  Megapixel = 1,000,000 pixels  Some common prefixes:  Kilo  Hecta- 100  Deka- 10  (base unit) 1  Deci- 0.1  Centi  Milli Nutrition labels often have some measurements listed in grams and milligrams

Measuring Temperature  Thermometer- 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 0ºC and boils at 100 ºC  ºC = 5 (ºF- 32) ºF = 9 ºC  The SI unit for temperature is the kelvin (K)  0K is the lowest possible temperature that can be reached.  In ºC, it is ºC  K = ºC + 273ºC = K – 273

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

 Primary conversion factor: 8848m ( 1km ) = km 1000m  Secondary conversion factor:  12 km (1000m) (1000mm) = 1.2 x 10 7 mm or 12,000,000 mm 1km 1m  Tertiary conversion factor:  5 km (1000m) ( 1hr ) = 1.39 m/sec 1 hr1 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 

Scientific Notation  Standard Notation – They way we are use to seeing numbers.  Example: Three hundred million = 300,000,000  Scientific Notation – A way of expressing a value as the product of a number between 1 and 10 and a power of 10.  Example: 300,000,000 = 3.0 x 10 8  The exponent 8 tells you the decimal point is really eight places to the right of 3.  Example: = 8.6 x  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  To add and subtract numbers they MUST have the same exponent, if they do not you need to write in standard notation and then put back to scientific notation Example: 8.6 x x & 8.6 x x  Multiplying & dividing  To multiply, 1 st multiple the coefficients then add the exponents. Example: 8 x X 6 x  To divide, 1 st divide the coefficients then subtract the exponents. Example: 8 x / 6 x 10 -5

Math Practice  Perform the following calculations. Express your answers in scientific notation.  (7.6 × 10 −4 m) × (1.5 × 10 7 m)  ÷ 29  2.Calculate how far light travels in 8.64 × 10 4 seconds. (Hint: The speed of light is about 3.0 × 10 8 m/s.)1.Perform the following calculations. Express your answers in scientific notation.  (7.6 × 10 −4 m) × (1.5 × 10 7 m)  ÷ 29

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

REVIEW Scientific Notation - Vocab  scientific notation –

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  Precision- 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 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 = g/cm cm 3  You must round to 3 significant figures: 7.86 g/cm 3

 Accuracy- 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.

Accuracy & Precision  

Error  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. Percent error 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: Nonzero numbers are always significant.  Rule 2: Zeros 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 infinite number of significant figures.

Sig Fig Practice

Sig Fig crash course 

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 → 2.53  Rule 2: If the digit to the right of the last significant figure is greater than 5, round up the last significant figure → 2.54  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 → 2.54  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 → → 2.52

Rounding Rounding Numbers Addition and subtraction  Round the answer to the same number of decimal places as the original measurement with the fewest decimal places. Multiplication and division  Round the answer to the same number of significant figures as the original measurement with the fewest significant figures.

 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 manipulated variable and the responding 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 y-variable  Run represents the corresponding change in the x-variable.

Direct proportion- Relationship in which the ratio of the two variables is constant. Inverse proportion- Relationship in which the product of the two variables is constant.

 Bar graphs and pie 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 -