Data Analysis

Si units Metric System Review

SI units Used in nearly every country in the world, the Metric System was devised by French scientists in the late 18th century. The goal of this effort was to produce a system that used the decimal system rather than fractions as well as a single unified system that could be used throughout the entire world.

In 1960, an international committee of scientists revised the metric system and renamed it the Systeme International d”Unites, which is abbreviated SI.

There are seven base units in SI There are seven base units in SI. A base unit is a defined unit in a system of measurement that is based on an object or event in the physical world.

The REAL kilogram, the International Prototype Kilogram (IPK) is kept in the International Bureau of Weights and Measures near Paris. Several official clones of this kilogram are kept in various locations around the globe.

A subset of the prefixes is Tera- (12), Giga- (9), Mega- (6), Micro- (-6), Nano- (-9), Pico- (-12), Femto- (-15), Atto- (-18): The Gooey Monster May Not Pick Five Apples.

Converting With SI (metric) When converting within the metric system it is simply a measure of moving the decimal in the appropriate direction.

Converting With SI (metric) Kangaroos Hop Down Mountains Drinking Chocolate Milk Kilo Hecto Deca Meter Deci Centi Milli 1000 100 10 1 .1 .01 .001 1000 m = ______ km .001 hg = ______ dg 42.7 L = _____ cL

Things to remember The short forms for metric units are called symbols, NOT abbreviations Metric symbols never end with a period unless they are the last word in a sentence. RIGHT: 20 mm, 10 kg WRONG: 20 mm., 10 kg. Metric symbols should be preceded by digits and a space must separate the digits from the symbols RIGHT: the box was 2 m wide WRONG: the box was 2m wide

Things to remember The short forms for metric units are called symbols, NOT abbreviations Metric symbols never end with a period unless they are the last word in a sentence. RIGHT: 20 mm, 10 kg WRONG: 20 mm., 10 kg. Metric symbols should be preceded by digits and a space must separate the digits from the symbols RIGHT: the box was 2 m wide WRONG: the box was 2m wide

Things to remember Symbols are always written in the singular form RIGHT: 500 hL, 43 kg WRONG: 500 hLs, 43 kgs BUT: It is correct to pluralize the written out metric unit names: 500 hectoliters, 43 kilograms The compound symbols must be written out with the appropriate mathematical sign included RIGHT: 30 km/h, 12 cm/s WRONG: 30 kmph, 30 kph (do NOT use a p to symbolize “per”) BUT: It is ok to write out “kilometers per hour”

Things to remember The meaning of a metric symbol is different depending on if it is lowercase or capitalized mm is millimeters (1/1000 meters) Mm is Megameters (1 million meters)

A unit that is defined by a combination of base units is called a derived unit. The derived unit for volume is the cubic centimeter (cm3), which is used to measure volume of solids, one cm3 is equal to 1 ml. 1000 mL is equal to 1 Liter.

Quantity measured Unit Symbol Relationship Length, width, distance, thickness, girth, etc. millimeter mm 10 mm = 1 cm centimeter cm 100 cm 1 m meter m   kilometer km 1 km 1000 m Mass (“weight”)* milligram mg 1000 mg 1 g gram g kilogram kg 1 kg 1000 g metric ton t 1 t 1000 kg Time second s Temperature degree Kelvin K Area square meter m² hectare ha 1 ha 10 000 m² square kilometer km² 1 km² 100 ha Volume milliliter mL 1000 mL 1 L cubic centimeter cm³ 1 cm³ 1 mL liter L 1000 L 1 m³ cubic meter m³

Another derived unit is Density is a ratio that compares the mass of a unit to its volume. The unit for density is g/ cm3 or kg/m3. Density = mass ÷ volume or Density = Mass Volume

Temperature Conversions Temperature is defined as the average kinetic energy of the particles in a sample of matter. The units for this are oC and Kelvin (K). Note that there is no degree symbol for Kelvin.

Heat is a measurement of the total kinetic energy of the particles in a sample of matter. The units for this are the calorie (cal) and the Joule (J).

The following equation can be used to convert temperatures from Celsius (t) to Kelvin (T) scales: T(K) = t(oC) + 273.15 You are simply adding 273.15 to your Celsius temperature. Example: Convert 25.00 oC to the Kelvin scale. T(K) = 25.00 oC + 273.15 = 298.15 b

Subtracting 273.15 allows conversion of a Kelvin temperature to a temperature on the Celsius scale. The equation is: t(oC) = T(K) - 273.15 You are simply subtracting 273.15 from your Kelvin temperature.

You are simply subtracting 273.15 from your Kelvin temperature. Convert the following from the Celsius scale to the Kelvin scale. 1. –200 oC 2. –100 oC 3. –50 oC 4. 10 oC 5. 50 oC 6. 37 oC 8. 100 oC 9. –300 oC 10. 300 oC 11. 273.15 oC 12. -273.15 oC

Convert the following form the Kelvin scale to the Celsius scale. 1. 0 K 2. 100 K 3. 150 K 4. 200 K 5. 273.15 K 6. 300 K 7. 400 K 8. 37 K 9. 450 K 10. –273.15 K

Using your calculator to perform math operations with scientific notation A calculator can make math operations with scientific notation much easier.  

Using your calculator to perform math operations with scientific notation A calculator can make math operations with scientific notation much easier. To add 6.02 x 10-2 and 3.01 x 10-3, simply type the following:   6.02 EXP +/- 2 + 3.01 EXP +/- 3   The calculator should read 6.321 –02. This means 6.321 x 10-2.

Using your calculator to perform math operations with scientific notation   Calculators vary. Instead of EXP, some have EE. Instead of +/-, some have (-). Only use the +/- or (-) if the exponent is negative.

 It is also important to keep in mind that when the EXP button is hit, it is as though the button said “x 10 to the.” THERE IS NO NEED TO PRESS THE MULTIPLICATION BUTTON (unless the numbers in the problem are being multiplied together).  

To multiply 6.02 x 10-2 and 3.01 x 10-3, simply type the following:   6.02 EXP +/- 2 x 3.01 EXP +/- 3 =  The calculator should read 1.812 02 -04. This means 1.812 02 x 10-4. If you are unsure, consult your teacher or the owner’s manual for the calculator.

Practice Section (3.37 x 104) + (2.29 x 105) (9.8 x 107) + (3.2 x 105) (8.6 x 104) – (7.6 x 103) (2.238 6 x 109) – (3.335 7 x 107) Multiplication and Division – Significant digits should be used in your answers!!!!!!! (1.2 x 103) x (3.3 x 105) (7.73 x 102) x (3.4 x 10-3) (9.9 x 106)  (3.3 x 103) 8. . (1.55 x 10-7)  (5.0 x 10-4)

Dimensional Analysis Dimensional analysis is the algebraic process of changing from one system of units to another. A fraction, called a conversion factor, is used. These fractions are obtained from an equivalence between two units.

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Dimensional Analysis For example, consider the equality 1 in. = 2.54 cm. This equality yields two conversion factors which both equal one:

Dimensional Analysis Note that the conversion factors above both equal one and that they are the inverse of one another. This enables you to convert between units in the equality. For example, to convert 5.08 cm to inches 5.08 cm x = 2.00 in

Dimensional Analysis For example, to convert 5.08 cm to inches 5.08 cm x = 2.00 in

USING DIMENSIONAL ANALYSIS You must develop the habit of including units with all measurements in calculations. Units are handled in calculations as any algebraic symbol: Numbers added or subtracted must have the same units.

Representing Data Graphing Circle Graph (pie chart) Useful for showing parts of a fixed whole.

Dimensional Analysis (Conversions) Units are multiplied as algebraic symbols. For example: 10 cm x 10 cm = 10 cm2 Units are cancelled in division if they are identical. For example, 27 g ÷ 2.7 g/cm3 = 10 cm3. Otherwise, they are left unchanged. For example, 27 g/10. cm3 = 2.7 g/cm3.

Dimensional Analysis (Conversions)

Dimensional Analysis (Conversions) Now use dimensional analysis to solve the following English to metric measurement conversion problems: (Use the equivalencies in the box on the previous page for your conversion factors). Remember to use units so that you can cancel the ones you don’t want in your answer and keep the ones that you do!

Dimensional Analysis (Conversions) 1. Convert 5.00 lb to g (2270 g)   2. Convert 8.00 in. to m ( 0.203 m)

Dimensional Analysis (Conversions) Try the rest of these on your own using dimensional analysis: Convert 3.00 lb to g   How many m are in 9.00 in?

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

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

Accuracy and Precision

Percent Error Ratio of an error to an accepted value Percent Error is a way of expressing how far off an experimental measurement is from the accepted/true value. The formula for it is:

Percent Error is a way of expressing how far off an experimental measurement is from the accepted/true value. The formula for it is:

A 9th grade physical science student finds the density of a piece of aluminum to be 2.54 g/cm3. The accepted value is 2.7 g/cm3. What is the percent error? Show your work and make sure that you have the correct number of significant digits.

A student measures the length of a cube of metal to be 2. 12 cm  A student measures the length of a cube of metal to be 2.12 cm. The actual length is 2.21 cm. What is the percent error? Show your work and make sure that you have the correct number of significant digits.

A student performs an experiment and calculates the strength of an acid as 0.015 8 M. The actual strength is 0.016 5 M . What is the percent error? Show your work and make sure that you have the correct number of significant digits.

Representing Data Graphing Bar Graph Useful for understanding trends. Works well with data in catagories. Often used to show how quantities vary with factors such as time, location, and temperature.

Representing Data Graphing Bar Graph Independent variable plotted on the x-axis Dependent variable plotted on the y- axis

Representing Data Graphing Line Graphs (two coordinate graphs) Most of the graphs used in chemistry Plot points have an x and y coordinate Independent variable plotted on the x-axis Dependent variable plotted on the y- axis

Line Graphs Best fit line (trend line) straight line drawn so as many points fall above the line as below the line.

Line Graphs Slope Positive slope - shows a direct relationship (e.g.as the IV increases the DV also increases) Negative slope - shows a direct relationship (e.g.as the IV increases the DV also increases)

Line Graphs Slope Positive slope - shows a direct relationship (e.g.as the IV increases the DV also increases) Negative slope - shows a direct relationship (e.g.as the IV increases the DV also increases)

Line Graphs Slope Positive slope - shows a direct relationship (e.g.as the IV increases the DV also increases) Negative slope - shows a direct relationship (e.g.as the IV increases the DV also increases)

Significant Figures (Sig Figs) Counting Significant Digits Quantities in chemistry are of two types: Exact numbers – These result from counting objects such as desks (there are 24 desks in this room), occur as defined values (there are 100 cm in 1 m), or as numbers in formulas (area of a right triangle = ½ B x H). They (24, 100, 1, and ½ for these examples) all have an infinite(∞) number of significant digits. B and H are measurements and do not have an infinite number of digits.

Inexact numbers – These are obtained from measurements and require judgment. Uncertainties exist in their values.

When making any measurement, always estimate one place past what is actually known. For example, if a meter stick has calibrations to the 0.1 cm, the measurement must be estimated to the 0.01 cm. When making a measurement with a digital readout, simply write down the measurement. The last digit is the estimated digit.

Significant digits are all digits in a number which are known with certainty plus one uncertain digit. The following rules can be used when determining the number of significant digits in a number:

The following rules can be used when determining the number of significant digits in a number: EXAMPLE SIG FIGS 1. All nonzero numbers are significant. 132.54 g 5 All zeros between nonzero numbers are significant. 130.0054 m 7 Zeros to the right of a nonzero digit but to the left of an understood decimal point are not significant unless shown by placing a decimal point at the end of the number. 190 000 mL 190 000. mL 2 6 All zeros to the right of a decimal point but to the left of a nonzero digit are NOT significant. 0.000 572 mg 3 All zeros to the right of a decimal point and to the right of a nonzero digit are significant. 460.000 dm

You can remember these rules or learn this very easy shortcut. If the number contains a decimal point, draw an arrow starting at the left through all zeros and up to the 1st nonzero digit. The digits remaining are significant. Try these: 0.002 5 1.002 5 0.002 500 0 14 100.0

If the quantity does not contain a decimal point, draw an arrow starting at the right through all zeroes up to the 1st nonzero digit. The digits remaining are significant. Try these: 225 10 004 14 100 103

A good way to remember which side to start on is: decimal point present, start at the Pacific decimal point absent, start at the Atlantic

1. 1.050 _____ 6. 420 000 ______ 2. 20.06 _____ 7. 970 ______ Practice Section - How many significant digits do each of the following numbers have? Practice Section - How many significant digits do each of the following numbers have? 1. 1.050 _____ 6. 420 000 ______ 2. 20.06 _____ 7. 970 ______ 3. 13 _____ 8. 0.002 ______ 4. 0.303 0 ____ 9. 0.007 80 _____ 5. 373.109 ____10. 145.55 _____

Homework Section How many significant digits do the following numbers possess? 0.02 0.020 501 501.0 5 000 5 000. 6 051.00 0.000 5 0.102 0 10 001 11. 20.03 kg 12. The 60 in the equality 60 s equals one min. 13. The one in the above. 14. 120 m 15. 10 dollar bills 16. 0.050 cL 17. The ½ in ½ mv2 18. 0.000 67 cm3

Rounding Rules Calculators often give answers with too many significant digits. It is often necessary to round off the answers to the correct number of significant digits. The last significant digit that you want to retain should be rounded up if the digit immediately to the right of it is (Each of the examples are being rounded to four sig digs):

Rounding Rules The last significant digit that you want to retain should be rounded up if the digit immediately to the right of it is Rule Example 4 sig digs ….. greater than 5 532.79 532.8 ….. 5, followed by a nonzero digit 17.255 1 17.26 ….. 5, not followed by a nonzero, but has an odd digit directly in front of it. 3 213.5 3214

Rounding Rules The last significant digit that you want to retain should stay the same if the digit immediately to the right of it is: Rule Example 4 sig digs ….. less than 5 5454.33 5454 ….. 5, not followed by a nonzero, but has an even digit directly in front of it. 0.00785 0.0078

Rounding Rules Practice Section - Round the following numbers to 3 sig digs. 1. 279.3 _________ 4. 32.395 ________ 7. 18.29 ___________ 2. 42.353 ________ 5. 32.25 ________ 8. 5 001 ___________ 3. 18.77 _________ 6. 7.535 _______ 9. 0.008 752 __________

Rounding Rules Homework Section - Round the following numbers to 4 significant digits 123 456 0.093 459 1.234 567 890 222.251 222.26 222.24 222.25 222.35 5 000 19.999

Line Graphs Slope Use data points to calculate the slope of the line. The slope is the change in y divided by the change in y.