Chapter 2
Measurements and Calculations

I: Scientific Method

Scientific method - definition
4 Steps in the scientific method

A: Observing and Collecting Data

Observing: definition
involves making measurements and collecting data

descriptive data - qualitative or non numeric
quantitative - numerical data


Experimenting - definition

The use of systems to learn more about matter.

B: Formulating a Hypothesis

hypothesis - definition

find relationships and patterns
make generalizations based on the data
organize data in tables
analyze data using statistics
use graphs and computers
use generalizations to formulate a hypothesis

a hypothesis serves as a basis for
a) making predictions and
b) for carrying out further experiments

C: Testing a Hypothesis
requires experimentation that provides data to support or refute a hypothesis;

Figure 2-3 page 31

If experimentation does not support the hypothesis it must be modified or discarded.


D: Theorizing

If hypothesis holds true then a model is developed.

May be visual, verbal, or mathematical.

May or may not become part of a theory.

Successful theories need to be able to predict the results of many new experiments.

Examples: atomic theory, kinetic molecular theory

Homework: 2.1


II: Units of Measurement

Measurement consists of a number and a unit.
This does not represents a quantity. A teaspoon represents a unit of measurement. The quantity is volume.

Early standards: foot, inch

A: SI Measurement

Adopted in 1960.

Seven base units and then derived units.

Standards of measurements - definition.

Ways of writing numbers. e.g. 100 000 not 100,000

Know table 2-1 page 34

Know table 2-2 page 35

B: SI Base Units

base unit with or without prefix

1: Mass

equivalent to 2.2 pounds

gram can be more useful in some instances

mass v weight

balance v scale

2: Length


equivalent to 39.37 inches



C: Derived SI Units

know table 2-3 page 36

Derived units - definition

Some combination units are given their own names e.g. a pascal (Pa)

1. Volume

volume - definition

cubic meter

100 cm in a meter

1 cubic meter = 100 x 100 x 100 = 1 000 000 cubic centimeters

1 cubic decimeter (dm) = 1 liter (L)

1 cubic decimeter = 1000 cubic centimeters

therefore 1 milliliter (mL) = 1 cubic centimeter (cc)

2. Density

density = mass/volume or m/v

units are kg/cubic meter -- inconvenient

usually g/cubic centimeter or g/milliliter -- for solids and liquids

usually kg/cubic meter or g/Liter for gases

density is a physical property

intensive property - can be one bit of information used to identify a substance

table 2-4 page 38

sample problem 2-1 page 39

D: Conversion Factors

conversion factor - definition

whether we write 4 quarters/ one dollar or
one dollar/4 quarters they are both equal to 1.

Thus we can use either one in our calculation -- which one is determined by what unit we want to cancel.

General format = given measurement x conversion factor

unit cancellation

1. Deriving Conversion Factors

You can derive conversion factors if you know the relationship between the units you have and the unit you want. SEE TABLE 2-1 p 34 & TABLE 2-2 p 35

Sample problem 2-2 p 41

Homework: 2.2

III: Using Scientific Measurements

A: Accuracy and Precision

Accuracy - definition

Precision - definition

Figure 2-8 page 44

1. Percent Error

formula for percent error

positive value if the accepted value is greater than experiment value

negative value if the accepted value is smaller than the experimental value

sample problem 2-3 page 45

2. Error in Measurement

affected by

a) skill of person doing the measurement

b) conditions under which measurement is done

c) the actual measuring instrument

Estimating because of the limitation of the instrument.

B: Significant Figures

significant figures - definition

figure 2-9 page 46

All digits including the uncertain one are significant.

Usually, the final digit is uncertain but significant.

Insignificant digits are never reported.

1. Determining the Number of Significant Figures

No zeroes: all digits shown are significant.

Have zeroes: position of zero is important.

Table 2-5 page 47

Sample problem 2-4 page 47

2. Rounding

Important when doing calculations - especially if using a calculator.

Can't show more significant figures than necessary.

Table 2-6 page 48 - skip last three rules

3. Addition or Subtraction with Significant Figures

When adding or subtracting decimals, the answer must have the same number of digits to the right of the decimal point as there are in the measurement having the fewest digits to the right of the decimal point.

4. Multiplication and Division with Significant Figures

e.g. calculating density using mass of 3.05 g and 8.47 mL

For multiplication and division the answer can have no more significant figures than are in the measurement with the fewest number of significant figures.

Sample problem 2-5 page 49

5. Conversion Factors and Significant Figures

Conversion factors are considered exact and so do not limit calculations by their significant figures.

e.g. to convert 4.608 m to cm using the conversion factor 100 cm/m, we would not limit our answer to three significant figures because of the 100 in 100cm/m.

We would express our answer with four significant figures to match the number of significant figures in 4.608 m.


C: Scientific Notation

form of scientific notation

When numbers are written in scientific notation only the significant figures are shown as the M

When converting a number to scientific notation:

a) Moving the decimal point to the right gives a negative exponent of 10.

b) Moving the decimal point to the left gives a positive exponent of 10.


1. Mathematical Operations Using Scientific Notation

a) Addition and Subtraction

both must have same exponent

if not adjust number so both have the same exponent

When done this, M's are added or subtracted, the x 10 remains the same and the exponent remains the same.

the units remain the same


2. Multiplication

multiply the M's

the x 10 remains the same

add the exponents algebraically

multiply the units e.g. cm x cm = cm squared

3. Division

divide the M's

x 10 remains the same

subtract the exponents algebraically (numerator minus the denominator)

units remain e.g. grams divided by mole = g/mole

D: Using Sample Problems

skip but expect the following:

show all given information

show conversion factor

set up problem

show unit cancellation

give answer with correct units

draw a box around the answer

E: Direct Proportion

direct proportion - definition

y/x = k or y = k x

graph of direct proportion

Table 2-7 page 55 and figure 2-11 page 55


F: Inverse Proportion

Inverse Proportion - definition

x y = k

type of graph

table 2-8 page 56 and figure 2-12 page 57

Homework: 2.3

 End of Notes

The scientific method is a logical approach to solving problems.

Observing is the use of senses to obtain information.

Experimenting is the carrying out of a procedure under controlled conditions to make observations and collect data.

A system is a specific portion of matter in a given region of space that has been selected for study during an experiment or observation.

A hypothesis is a testable statement.

A model is an explanation of how phenomena occur and how data or events are related.

A theory is a broad generalization that explains a body of facts or phenomena.

Quantity is something that has magnitude, size or amount.

Standards of measurement are of constant value, easy to preserve and reproduce, and practical in size.

Mass is the amount of matter in an object. ba

Weight is a measure of the gravitational pull on matter.

Derived units are combinations of SI base units.

Volume is the amount of space occupied by an object.

A conversion factor is a ratio derived from the equality between two different units that can be used to convert from one unit to the other.

Accuracy refers to the closeness of measurements to the correct or accepted value of the quantity measured.

Precision refers to the closeness of a set of measurements of the same quantity made in the same way.

Significant figures in a measurement consist of all the digits known with certainty plus one final digit, which is somewhat uncertain or is estimated.

Form of Scientific Notation
M x 10n

a) M represents the significant figure of the measurement;
b) n represents the number of places the decimal point was moved to get the measurement into scientific notation format;
c) x 10 is always present in scientific notation.

Two quantities are directly proportional to each other if dividing one by the other gives a constant value.
y/x = k or
y = k x

Two quantities are inversely proportional to each other if their product is constant.

Percent error = ((accepted value - experimental value)/ accepted value) x 100