Chapter 2Data Analysis

I. SI Units• Scientists adopted a system of standard

units so all scientists could report data that could be reproduced and understood by others

- The revised system is called the Système Internationale d’Unités, SI

A. Base Units (7)• The metric system is a decimal system• A base unit is a defined unit in a system of

measurement, i.e. time, length, mass, temperature, etc.

• Prefixes describe the range of possible measurements above or below the base unit as multiples or factors of ten, respectively (p. 26)

DD

1. Time, base unit = second (s)• One second is equal to the frequency of

microwave radiation given off by a cesium-133 atom

2. Length, base unit = meter (m)• One meter is equal to the distance that

light travels through a vacuum in 1/299,792,458 of a second

3. Mass, base unit = kilogram (kg)

4. Temperature, base unit = kelvin (K)• The Celsius scale is also used - it defines temperatures at

which water freezes, 0°C, and boils, 100°C

- the distance between these points are divided into 100 equal units, or degrees, Celsius

• Celsius is converted to the Kelvin scale by the equationdegrees Celsius + 273 = Kelvins

5. Amount of a substance, base unit = mole (mol)

6. Electric current, base unit = ampere (A)7. Luminous intensity, base unit = candela (cd)

B. Derived Units• Units that are defined by a combination of

base units1. Speed, SI unit = meters per second (m/s)

(Length/time)2. Volume, SI unit = cubit meter (m3)• Cubic decimeter (dm3) or cubic

centimeter (cm3) for smaller volumes

1m3 = 1000 L1dm3 = 1L1cm3 = 1mL

• The volume of irregular objects can be found by the displacement of water

3. Density, SI unit = grams per cubic centimeter (g/cm3) or (g/mL)• Density measures how much mass is

packed into a given volume• Density = mass/volume• Density can be used to identify an unknown

sample of matter, or element - each element has its own density

II. Scientific Notation• Numbers that are extremely small or large

are converted into condensed numbers using scientific notation

• Scientific notation expresses numbers in a multiple of two factors

0.000000000000278 = 2.78x10-13

156,000,000,000,000,000,000 = 1.56x1020

1. A number between 1 and 102. A ten raised to a power, or exponent• The exponent tells you how many times the

first factor must be multiplied by ten• When the exponent is positive, the number

is larger than 1• When the exponent is negative, the

number is less than 1

A. Adding and Subtracting using scientific notation• The units must be the same• Exponents of all numbers being added or

subtracted must be expressed to the same power of ten

B. Multiplying and dividing using scientific notation

1. When multiplying, multiply the first factors and then add the exponents

2. When dividing, divide the first factors and then subtract the exponent of the divisor from the exponent of the dividend

III. Dimensional Analysis• When adding and subtracting different units,

one number must be converted so its units match that of the other number

• A conversion factor is a ratio of equivalent values used to express the same quantity in different units

- conversion factors change the units of a quantity without changing its value

• Dimensional analysis is a method of problem-solving that often uses conversion factors to focus on the units used to describe matter

2 Cups = 1 Pint2 Pints = I Quart4 Quarts = 1 Gallon

IV. Measurements A. Accuracy and Precision 1. Accuracy refers to how close a measured

value is to the accepted value

2. Precision refers to how close a series of measurements are to one another

B. Percent Error• Data collected in an experiment are

experimental values• There are often values that are always

considered true, called accepted values (p.914-916)

i.e. densities, melting points, boiling points• Accuracy of experimental data can be

evaluated by calculating the error, or difference between experimental and accepted values

Error = experimental value - accepted value

• Percent error is the ratio of an error to an accepted valuePercent error = error/accepted value X 100

V. Significant Figures• Scientists indicate the precision of

measurements by the number of digits they report

- as scientists have developed better measuring devises, they have been able to make more precise measurements

- a value of 3.52 g is more precise than a value of 3.5g

• The digits that are reported are called significant figures (sig.figs.)

• Significant figures include all known digits plus one estimated digit

i.e. you have to estimate the digit between millimeter tick marks on a centimeter ruler

• There are 5 rules for recognizing significant figures

1. Non-zero numbers are always significant72.3 g = 3 sig.figs.

2. Zeros between non-zero numbers are always significant

60.5 g = 3 sig.figs.

3. All final zeros to the right of the decimal place are significant

6.20 g = 3 sig.figs.

4. Zeros that act as placeholders are not significant. Convert quantities to scientific notation to remove the placeholder zeros

0.0253 g = 2.53 g x10-2 = 3 sig.figs4320 g = 4.32 g x 103 = 3 sig.figs

5. Counting numbers and defined constants have an infinite number of significant figures

VI. Rounding off Numbers• The answer to any calculation should have

no more significant figures than the data with the fewest significant figures

• There are 4 rules for rounding significant figure numbers

1. If the digit to the immediate right of the last significant figure is less than five, do not change the last significant figure

5.33 = 5.3

Remainsthe same

2. If the digit to the immediate right of the last significant figure is greater than five, round up the last significant figure

5.37 = 5.4

Increasesby one

3. If the digit to the immediate right of the last significant figure is equal to five and is followed by a nonzero digit, round up the last significant figure

5.351 = 5.4

Increasesby one

4. If the digit to the immediate right of the last significant figure is equal to five and is followed by a zero, look at the last significant figure. If it is an odd digit, round it up, if it is an even digit, do not round up

5.350 = 5.4

Increasesby one

5.250 = 5.2

Remainsthe same

A. Addition and Subtraction• Your answer must have the same number

of digits to the right of the decimal point as the value with the fewest digits to the right of the decimal point

B. Multiplication and Division• Your answer must have the same number

of significant figures as the measurement with the fewest significant figures