Analyzing Data

Units and Measurements

Units Système Internationale D’Unités▪ Units were not always exact▪ Scientists report data, and this data should be

reproducible by other scientists▪ A need for standard units was acknowledged

▪ 1960, an international committee of scientists met to update the existing metric system▪ The revised system is called the Système

Internationale D’Unités AKA SI

Base Units and SI Prefixes Base Unit – is a defined unit a system

of measurement that is based on an object or event in the physical world▪ Independent of other units▪ Time – seconds (s)▪ Length – meter (m)▪ Mass – kilogram (kg)▪ Temperature – kelvin (K)▪ Amount of a substance – mole (mol)▪ Electric current – ampere (A)▪ Luminous intensity – candela (cd)

Base Units and Prefixes Time▪ SI base unit is second (s)▪ Physical standard used to define the second

is the frequency of the radiation given off by a cesium-133 atom▪ Cesium based clocks are used when highly

accurate timekeeping is required▪ Many chemical reactions take place within a

fraction of a second

Base Units and SI Prefixes Length▪ SI base unit is meter (m)▪ A meter is the distance that light travels in a

vacuum in 1/299,792,458 of a second▪ A meter is close to a yard

Base Units and SI Prefixes Mass▪ SI base unit is kilogram (kg)▪ A platinum and iridium cylinder kept in

France defines the kilogram▪ The cylinder is kept in a vacuum under a triple bell

jar to prevent oxidation

▪ About 2.2 pounds

Base Units and SI Prefixes Prefixes (refer to table 2.2)▪ Giga▪ Mega▪ Kilo▪ Deci▪ Centi▪ Milli ▪ Micro▪ Nano▪ Pico

Base Units and SI Prefixes Temperature▪ A quantitative measurement of the average

kinetic energy of the particles that make up an object▪ As particles in motion in an object increase,

so does temperature▪ Three scales have been developed

Base Units and SI Prefixes Temperature

▪ Fahrenheit °F Used in the US Gabriel Daniel Fahrenheit (German scientist)

devised it in 1724 Water freezes at 32°F Water boils at 212°F

Base Units and SI Prefixes Temperature

▪ Kelvin▪ K; SI unit▪ William Thomson, known as Lord Kelvin (Scottish

physicist and mathematician) devised kelvin▪ 0K is the lowest possible energy state▪ Water freezes 273.15K▪ Water boils 373.15K▪ K = °C + 273

Derived Units Derived Unit – a unit that is defined by a

combination of base units▪ Volume – the space occupied by an object▪ Found by multiplying the length, width, and depth▪ m3

▪ Liter – is equal to one cubic decimeter; commonly used

▪ Density – a physical property

Derived Units▪ Density – a physical property of matter and is

defined as the amount of mass per unit volume▪ Gram per cubic centimeter for solids▪ Gram per cubic milliliter for gases or liquids▪ Density = mass/volume

Scientific Notation and Dimensional Analysis

Scientific Notation Scientific Notation – can be used to

express any number as a number between 1 and 10 (known as the coefficient) multiplied by 10 raised to a power (known as an exponent).▪ Addition and subtraction▪ Exponents must be the same

▪ Multiplication and Division▪ First, multiply or divide coefficients▪ Second, add or subtract exponents▪ Third, rewrite into scientific notation if needed

Dimensional Analysis Dimensional Analysis – is a systematic

approach to problem solving that uses conversion factors to move, or convert, from one unit to another

Conversion Factor – a ratio of equivalent values having different units

Uncertainty in Data

Accuracy and 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 and Percent Error Error – is defined as the difference

between an experimental value and an accepted value▪ Error = experimental value – accepted value

Percent Error – expresses error as a percentage of the accepted value▪ Percent Error = ____Ι error Ι______ x 100

accepted value

Significant Figures Significant Figures – include all known

digits plus one estimated digit▪ Nonzero numbers are always significant▪ Zeros between nonzero numbers are always

significant▪ Placeholder zeroes are not significant. To

remove placeholder zeroes write the number in scientific notation▪ Counting number and defined constants have

an infinite number of significant figures

Rounding Numbers Based on number of significant figures Calculators won’t do this for you Addition and Subtraction▪ Answer must have the same # of digits to the

right of the decimal as the original value having the fewest number of digits to the right of the decimal

Multiplication and Division▪ Answer must have the same # of sig figs as the

measurement with the fewest amount of sig figs

Representing Data

Graphing Graph – is a visual display of data▪ Circle Graph (Pie Chart)▪ Show parts of a whole

Graphing Bar Graphs▪ Often used to show how a quantity varies

across categories

Graphing Line Graphs▪ In chemistry most graphs you create, will

interpolate between the lines.▪ Independent Variable – plotted on the X-axis▪ Dependent Variable – plotted on the Y-axis▪ Relationship between variables▪ If best fit is a straight line – linear relationship

Graphing Line Graphs▪ Relationship between variables▪ If best fit is a straight line – linear relationship

Rises to the right – positive Sinks to the right – negative

▪ Slope = rise/run▪ Slope= Δy/Δx

Interpreting Graphs Interpolation and extrapolation▪ Continuous data allows you to read the value

from any point that fall between the recorded data points. This is called interpolation.▪ You can also extend a line beyond the plotted

points, and this is called extrapolation.▪ You must be careful, because it can easily lead to

errors and inaccurate predictions.