Scientific Measurement & Data Analysis Chapter 2 Scientific Measurement & Data Analysis

It depends upon the units!!! Units of Measurement Which is bigger? 5 or 120 5 quarters and 120 pennies 5 pennies and 120 quarters It depends upon the units!!!

Units of Measurement – English English – Developed from common use. Lacks uniformity Lacks coherency Not easy to use Metric – Developed in France in 1795. Simple base units Interchangeable prefixes Decimal (base 10) system

Metric Prefixes Prefix Symbol Meaning kilo- k hecto- h deca- da deci- centi- c milli- m 1000 1 km = 1000 m 100 1 hm = 100 m 10 1 dam = 10 m .1 10 dm = 1 m .01 100 cm = 1 m .001 1000 mm = 1 m

Making Metric Your Own When you see Think of Liter (L) half a 2L pop meter (m) inches longer than a yard stick decimeter (dm) length of a pack of gum centimeter (cm) thickness of a pack of gum millimeter (mm) thickness of DVD kilometer (km) more than 1/2 a mile (about .6) gram (g) less than half a dime

Units of Measurement – History SI (International System of Units) – Developed by scientists in 1960. Only 7 fundamental units Derived units based on fundamental units

Units of Measurement – SI Base Units Quantity Unit Symbol Length meter m Mass kilogram kg Time second s Temperature kelvin K Amount of Substance mole mol Electrical current ampere A Luminous intensity candela cd

kilogram per cubic meter Units of Measurement – SI Derived Units Quantity Unit Symbol Derivation Units Area square meter m2 length  width m  m Volume cubic meter m3 length  width  height m  m  m Density kilogram per cubic meter kg/m3 mass volume kg Velocity meter per second m/s length/time m s Force newton N (mass  length) (time  time) kg  m s2 Pressure pascal Pa force area N = kg m2 m  s2 Energy joule J force  length N  m = kg  m2

Metric Conversions kilo- hecto deca- base unit deci- centi- milli- (k) (h) (da) (d) (c) (m) Meter (m) Liter (L) Gram (g) Second (s) 1000 100 10 1/10 1/100 1/1000 To convert from 1 prefix to another, just move the decimal to the left or right that many places!

5000 cg How many centigrams (cg) are in 5dag? 1 2 3 kilo- hecto deca- base unit deci- centi- milli- (k) (h) (da) (d) (c) (m) Meter (m) Liter (L) Gram (g) Second (s) How many centigrams (cg) are in 5dag? Just move the decimal ___ places to the ________! 5 3 right 5000 cg

.012 km 1 2 3 left How many kilometers (km) are in 12 meters m? kilo- hecto deca- base unit deci- centi- milli- (k) (h) (da) (d) (c) (m) Meter (m) Liter (L) Gram (g) Second (s) How many kilometers (km) are in 12 meters m? Just move the decimal ___ places to the ________! 1 2 3 left .012 km

Scientific Notation Scientific Notation 1100000 m = 1.1 × 106 m exponent coefficient (Integer) ( 1 and  10) 0.000000023 g = 2.3 × 10-8 g

How reliable are Measurements? Accuracy, Precision Accuracy – how close a measurement is to the true value. Precision – how close a group of measurements are to each other.

How reliable are Measurements? How do you make a measurement? With most measuring devices, you should be able to estimate to one decimal place more than the smallest division on the device. The smallest division is a _____ of a centimeter, so you can guess to the __________ (or ___ decimal places like 1.24). tenth hundredth 2

Using A Ruler = 1.94 cm = 3.00 cm = 1.5 cm

1 2 3 1 = 5.73 mL 2 = 3.0 mL 3 = .35 mL

Measurement – Significant Figures All of the known digits plus the estimated digit are significant – they are not placeholders. When we measured the volume of cylinder 1 on the last slide we got: 5.73 mL known estimated This would mean 3 significant figures.

100 200 300 100 200 300 120 mL 120 mL

Measurement – Significant Figures Significant Figure Rules Every nonzero is significant. 123.2 g Zeros between nonzero digits are significant. 1004 m Zeros to left of nonzero are NOT significant. 0.01 g 4 sig figs 4 sig figs 1 sig figs

Measurement – Significant Figures 4. Zeros to the right of nonzero digits are significant ONLY when the decimal is shown. 12.00 m 1200. m 1200 m 1.20 ×103 m 5. Counting numbers and defined quantities have unlimited significant digits. 3 gold atoms unlimited 1 hour = 60 minutes 1 and 60 unlimited 4 sig figs 4 sig figs 2 sig figs 3 sig figs

Significant Figures in Calculations An answer can’t have more significance than the measurements upon which it is based. YOUR ANSWER IS ONLY AS GOOD AS YOUR WORST MEASUREMENT!

Significant Figures in Calculations Addition Subtraction Round your answer to the same number of decimal places as your least significant number. Think of it as the leftmost uncertainty. 124.0 m + .12 m 420 m 544.12 m 540 m

Significant Figures in Calculations Multiplication and Division Round answer to the same number of significant digits as the measurement with the least number of significant digits. 238.63 m × 12.0 m 5 3 2863.56 m2 2860 m2

Temperature What does your body sense? temperature or heat What contains more heat? a glass of boiling water or an iceberg What does your body sense? temperature or heat

Temperature Heat – type of energy transferred because of a difference in temperature. Can’t be measured directly Temperature – measure of the average kinetic energy of the particles in a sample of matter. Determines the direction of heat transfer

Temperature Scales Fahrenheit (F) – zero based on equal mix of snow and ammonium chloride. 32F = freezing point of water 212F = boiling point of water Celsius (C) – based on water 0C = freezing point of water 100C = boiling point of water

Temperature Scales Kelvin (K) - only temperature scales that is proportional to the speed of the particles. 0 K = all particle motion stops 273 K = freezing point of water 373 K = boiling point of water

Temperature Conversion T(K) = T(C) + 273 T(C) = T(K) – 273 What is 25C (room temp.) in Kelvin? T(K) = 25C + 273 = 298 K

Density mass Density volume = The density of water is 1.00 g/mL!!! D M

Density - Problem mass = (2.7 g/mL) × (19.5 mL – 12.4 mL) A piece of aluminum (density 2.7 g/mL) is added to a graduated cylinder with 12.4 mL of water in it. The volume of the water rises to 19.5 mL, what is the mass of the aluminum? D M V (volume) (volume) mass = (2.7 g/mL) × (19.5 mL – 12.4 mL) mass = (2.7 g/mL)(7.1 mL) mass = 19.17 g 19g

How reliable are Measurements? Error (measuring experimental accuracy) Error = accepted value – experimental value Percent Error = |error| accepted value × 100

How reliable are Measurements? Experimentally, the boiling point of a substance is found to be 99.12 °C. The actual value of the substance is 100.0 °C. Find the error and percent error of the measured value. 100.0 °C 99.12 °C .88 °C - Error = accepted - experimental = 100.0 °C - 99.12 °C = .88 °C .9 °C = .9 °C × 100 100.0 °C % error = |error| × 100 accepted = .9%

Graphing Using data to create a graph can help to reveal a pattern if one exists. A graph is a visual display of data.

Circle Graph A circle graph is sometimes called a pie chart because it is divided into wedges like a pie or pizza. A circle graph is useful for showing parts of a fixed whole. The parts are usually labeled as percents with the circle as a whole representing 100%.

Bar Graph A bar graph often is used to show how a quantity varies with factors such as time, location, or temperature. In those cases, the quantity being measured appears on the vertical axis (y-axis). The independent variable appears on the horizontal axis (x-axis). The relative heights of the bars show how the quantity varies.

Line Graph In chemistry, most graphs that you create and interpret will be line graphs. The points on a line graph represent the intersection of data for two variables. The dependent variable is plotted on the y-axis and the independent variable on the x-axis. Remember that the independent variable is the variable that a scientist deliberately changes during an experiment.

Line Graph Sometimes points are scattered, the line cannot pass through all the data points. The line must be drawn so that about as many points fall above the line as fall below it. This line is called a best fit line.

Line Graph If the best fit line is straight, there is a linear relationship between the variables and the variables are directly related. This relationship can be further described by the steepness, or slope, of the line. If the line rises to the right, the slope is positive. A positive slope indicates that the dependent variable increases as the independent variable increases.

Line Graph If the line sinks to the right, the slope is negative. A negative slope indicates that the dependent variable decreases as the independent variable increases.

Line Graph Either way, the slope of the graph is constant. You can use the data points to calculate the slope of the line. The slope is the change in y divided by the change in x.

Interpreting Graphs An organized approach can help you understand the information on a graph. First, identify the independent and dependent variables. Look at the ranges of the data and consider what measurements were taken. If a graph has multiple lines or regions, study one area at a time. Decide if the relationship between the variables is linear or nonlinear. If the relationship is linear, is the slope positive or negative?

Interpreting Graphs When points on a line graph are connected, the data is considered continuous. You can read data from a graph that falls between measured points. This process is called interpolation.

Interpreting Graphs You can extend the line beyond the plotted points and estimate values for the variables. This process is called extrapolation. Why might extrapolation be less reliable than interpolation? The trend might change!