Measurement &

Problem Solving

Scientific Method

The scientific method is a logical approach to solving problems by observing and collecting data, formulating hypotheses, testing hypotheses, and formulating theories that are supported by data.

I. Qualitative vs. Quantitative

Measurements

Qualitative Measurement

1). Qualitative measurement = a measurement that gives descriptive, NONnumeric results

a) Ex: Jillian ran a fast race.

b) Ex: The light was green

Quantitative Measurement

2) Quantitative measurement = a measurement that gives results in definite form, usually in numbers and units

a) Ex: Jeff finished his race in 54.3 seconds

b) Ex: the light had a wavelength of 505 nanometers.

Variables

Independent variables

Dependent variables

Control variables

II. “SI” System

1) SI System = a modernized form of the metric system used by scientists

A. Fundamental SI Units

1) Fundamental unit = a unit that is defined by a single standard of measurement

Fundamental SI Units(There are seven fundamental SI units)

A. Fundamental SI Units

3) Length = a measure of linear distance; the fundamental SI unit of length is the meter (m)

a) The distance light travels in a vacuum during a time interval of 1/299792458 of a second is the SI standard for one meter

A. Fundamental SI Units

4) Mass = a measure of the quantity of matter in a sample; the fundamental SI unit of mass is the kilogram (kg); the abbreviation for gram is “g”

a) A platinum-iridium cylinder kept at the International Bureau of Weights and

Measures in the French town of Sevres is the SI standard for one kilogram

A. Fundamental SI Units

b) Weight = a measure of the gravitational pull on matter

A. Fundamental SI Units

5) Time = a measure of the interval between occurrences; the fundamental SI unit of time is the second (s)

a) The duration of 9,192,631,770 periods of particular radiation emitted by cesium-133 atoms is the SI standard for one second.

B. Derived Unit

1) Derived unit = a unit that can be obtained from combinations of fundamental units

Examples of Derived SI Units

B. Derived Unit

3) Volume = a measure of the amount of space occupied by a sample of matter; the derived SI unit of volume is the cubic meter (m3)

a) Chemists often use a non-SI unit for volume, the liter (L)

b) 1 dm3 = 1 L

c) 1 cm3 = 1mL

C. Prefixes

1) Other SI units are obtained by combining prefixes with a root unit. The prefixes represent multiples or fractions of 10. The following table lists some prefixes:

Prefixes Used with SI Units

D. Prefixes Used with SI Units

Write the correct abbreviation for each of the following units.

a) Kilosecond ______________

b) Hectogram ______________

c) Dekaliter _______________

d) Deciliter ______________

e) Centimeter _______________

f) Milligram ______________

cm

dL

mg

daLhgks

E. Conversions(Ladder Method)

Try these conversions, using the ladder method

a) 1000 mg = ___________ g

b) 160 cm = ____________ mm

c) 109 g = _____________ kg

d) 1 L = _____________ mL

e) 14 km = _____________ m

f) 250 m = ______________ km

1.0

0.109

1,000

14,0000.250

1,600

F. Other Useful Conversions

1) Some English System Conversions (exact conversions):

1 foot (ft) = 12 inches (in) 1 pound (lb) = 16 ounces (oz)

1 yard (yd) = 3 feet (ft) 1 ton = 2000 pounds (lb)

1 mile (mi) = 5280 feet (ft)

1 quart (qt) = 32 fluid ounces (fl oz)

1 quart (qt) = 2 pints (pt)

1 gallon (gal) = 4 quarts (qt)

2) Some conversions between systems:

1 inch (in) = 2.54 centimeters (cm)

1 pound (lb) = 453.59 grams (g)

1 gallon (gal) = 3.7854 liters (L)

III. Scientific Notation

1)4.6 x 103 m =

4.6 m x 10 x 10 x 10 =

4600 m

2) 5.4 x 10-3 m =

5.4 m ÷ 10 ÷ 10 ÷ 10 =

0.0054 m

3) For numbers expressed in scientific notation, the decimal

place goes after the first nonzero digit.

4) Write each of the following numbers in scientific notation.

a)0.000347 g = ________________

b)289,302 km = ________________

c)0.00004477 mm = _______________

3.47 x 10-4 g 2.89302 x 105

km 4.477 x 10-5 mm

5) Write each of the following numbers in ordinary notation.

a)8.95 x 104 m = _________________

b)4.796 x 10-5 hm = _______________

c)2.73 x 105 cm = _________________

89,500 m

0.00004796 hm 273,000

cm

Significant Figures

IV. Taking Measurements

1) Review the proper way to measure using a ruler,

graduated cylinder, thermometer, etc.

IV. Taking MeasurementsMeniscus = the curvature of a liquid in a container because of surface tension.

Your eye should be level with the top of the liquid and you should read the bottom of the meniscus.

V. Precision, Accuracy and Percent Error:

1)Precision = a measure of how close a series of measurements are to one another

a) It takes a series of measurements to determine precision

V. Precision, Accuracy and Percent Error:

2) Accuracy = a measure of how close a measurement comes to the true or accepted value of what is measured

3) Bull’s Eye Analogy

V. Precision, Accuracy and Percent Error:

4) Percent error = the difference between the measured quantity and the accepted value, expressed as a percentage of the accepted value

Percent Error Formula: Value accepted - Valueexperimental

% error = Value accepted x 100

5) Gary measured the density of a piece of lead to be 12.12 g/cm3. The accepted value for the density of lead is 11.35 g/cm3. Calculate the percent error.

VI. Problem Solving

1) Approach to solving problems

a) Analyze:

1) Read the problem carefully at least twice.

2) Identify what you know and what you are trying to find.

3) Include units.

VI. Problem Solvingb) Plan:

1) Graphs, pictures, graphic organizers, flowcharts, or other visual aids may be helpful.

2) Identify formulas and/or conversion factors that will be used.

3) Be certain that “units will cancel” as needed.

4) Solve formulas for an unknown variable before putting in values.

5) Set-up the problem

VI. Problem Solvingc) Compute:

1) Plug in given information, conversion factors, and other necessary values. Include units on all numbers!!

2) Cancel units properly.

3) Calculate the answer.

VI. Problem Solving

d) Evaluate:

1) Is the answer reasonable?

2) Is the same answer obtained after rechecking?

3) Do the units cancel correctly so the answer has the proper units?

4) Have all parts of the question be answered?

VII. Density:

1) What is heavier, a pound of lead or a pound of cork?

Neither, they both weigh a pound!!!Lead is MORE DENSE

VII. Density:

2) What floats in water, lead or cork? Why?

Cork floats in water because it is LESS dense than water

VII. Density:

Take a look at the two boxes below. Each box has the same volume. If each ball has the same mass, which box would weigh more? Why?

VII. Density:

The box that has more balls has more mass per unit of volume.

This property of matter is called DENSITY.

VII. Density:

4) Density = a property of matter representing the mass per unit volume.

a) The derived SI unit of density: kg/m3

b) Other commonly used density units, g/cm3, g/mL, g/L

VII. Density:

c) Volumes can change with temperature, therefore, densities also change with temperature.

Ex: Increasing the temperature of a gas would also increase the volume of the gas. Therefore the temperature of the gas, affects the density of the gas!

VII. Density:

d) Formula:

Density = Mass__

Volume

Or D = M

V

VII. Density:

5) Solve the density formula for mass.

VII. Density:

6) Solve the density formula for volume.

7) A sample of aluminum metal has a mass of 8.4g. The volume of the sample is 3.1cm3.

Calculate the density of aluminum.

8) Diamond has a density of 3.26 g/cm3. What is the mass of a 0.350 cm3 of

diamond?

9) Suppose a scientist collects 76.2g of mercury. Calculate the volume given

that the density of mercury is 13.6 g/mL.