SOLVING PROBLEMS USING A SCIENTIFIC APPROACH (pp. 8 – 14)
Scientific Method
1. Since any number of scientists around the world can choose to investigate a problem, it would be helpful if they all used common procedures.
2. The way scientists carry out experiments or investigations is referred to as the ______.
3. The scientific method is a logical approach to exploring a problem or question that has been raised through observation.
4. This approach is designed to produce a solution or answer that can be tested, retested, and supported by experimentation.
5. The fundamental activities of the scientific method are:
-Make observations and collect data that can lead to a question. Define the problem. Is it ______or ______?
-Formulate and objectively test hypotheses by experiments.
-Interpret results and revise the hypothesis if necessary.
-State conclusions in a form that can be evaluated by others.
Variables
1. In order to write a good hypothesis to test we need to understand the variables involved.
2. Variables are factors, conditions, and/or relationships that can change or be changed in the experiment.
3. In a scientific investigation there are four kinds of variables:
- The ______variable is a factor or condition that is intentionally changed during the experiment.
- The ______variable is a factor or condition that might be affected as a result of that change.
- A ______variable is a factor or condition that is not changed.
- A ______is a standard used for comparison.
***** List the variable for the following problem and identify both the independent and dependent variables.
PROBLEM: Determine the % water in a chemical compound
Hypothesis
1. A ______is a proposition based on certain assumptions that can be evaluated scientifically.
2. It is usually written in the form of an ______statement.
3. Steps for writing a good hypothesis:
- Identify variables in a given event or relationship.
- Identify a pair of variables that might logically be related.
- Identify the independent and dependent variable.
- Write the hypothesis.
***** Write a hypothesis for our problem:
Independent variable:
Dependent variable:
Hypothesis:
Experiment
- An ______is a process carried out under controlled conditions to test the validity of a hypothesis.
2. By carefully controlling variables, researchers can identify the dependent variable and its relationship with the other variables.
3. An experiment plan would include the following:
Theory
1. Any conclusion scientists make must come directly and solely from the data they obtain in their experiment. The data and results may, or may not, support their hypothesis.
- Any hypothesis that withstands repeated testing may become part of a ______.
- A theory is an explanation of an observation that is based on experimentation and reasoning.
- A theory is not a fact; it is an explanation. Theories can be adjusted as new information comes to light.
Laws
- Certain facts in science always hold true. Such facts are labeled as ______.
- A scientific law is a statement or mathematical expression describing the behavior of the natural world.
- There are a limited number of laws in science compared to the number of theories or hypotheses.
- A hypothesis ______an event; a theory ______it; and a law ______it.
HOW SHOULD DATA BE REPORTED?(pp. 113 – 130)
Significant Figures and Standard Units
1. Observations and properties can be described most exactly in numerical terms. You can describe a person’s characteristics such as height, mass or age using words such as:
2. These descriptions are very subjective and vague. Numbers are more useful and make the descriptions more exact.
3. In this section we will study how data should be reported in terms of significant figures and standard units.
Significant Figures
1. If a measurement is reported with either too many or too few digits, it is not possible to tell how precise the measurement really is. To indicate precision, significant figures are used.
2. Significant figures are those digits in a measurement that have actually been measured by comparison with a scale, plus one estimated digit.
3. The number of significant figures you obtain is limited by how finely divided your measuring scale is.
Rules for Significant Figures
1. All nonzero digits are significant. Examples:
2. All zeros that fall between nonzero digits are significant. Examples:
3. Zeros to the left of the first nonzero digit (leading zeros) in a number are ______significant; they merely help indicate the position of the decimal point. Examples:
4. When a number ends in zeros (trailing zeros) that are to the right of a decimal point, they ______significant. Examples:
5. When a number ends in zeros that are not to the right of a decimal point, the zeros may or may not be significant. They are not normally considered significant. Examples:
6. Exact numbers. Often calculations involve numbers that were not obtained by using measuring devices but were determined by counting such as ______or ______. Such numbers are called exact numbers. They can be assumed to have an unlimited number of significant figures.
7. Exact numbers can also arise from definitions. For example, 1-inch = 2.54 centimeters. Neither 2.54 nor 1 will have any effect on limiting the number of significant figures when used in a calculation.
8. The rules for significant figures also apply to numbers written in scientific notation:
9. In paragraph 5 it is hard to tell whether zeros to the right of a nonzero digit, but not to the right of a decimal point, are significant. There are two ways you can write such numbers so you can tell whether such zeros are significant:
- place a decimal point after the zeros that are significant
- use scientific notation
***** Determine the number of significant figures in each of the following:
503635.526500.
6300.0001510,001
2.407601
Rounding Numbers
1. Before we can apply the rules for significant figures to calculations, we need to look at the procedures for rounding numbers.
2. If the digit to be removed is 5 or greater, the preceding number is ______by one.
3. If the digit to be removed is less than 5, then the preceding number is ______.
***** Round each of the following measurements to three significant figures:
24.5903.00267.963
24.353956.789
Calculations
1. Each measured quantity has some degree of error in it. When measurements are added, subtracted, multiplied and divided small error may either cancel each other or add up to a larger error.
2. To avoid the possibility of adding extra error, rules for significant figures are used in calculations. The rules for addition and subtractions are different from the rules for multiplication and division.
3. When adding or subtracting: The answer can have no more digits to the right of the decimal point than there are in the measurement with the smallest number of digits to the right of the decimal point.
***** Add the following number together and round the answer to the proper number of significant figures:
3.95 + 2.879 + 213.6
83 – 20.4
4. When multiplying or dividing: The answer can have no more significant figures than there are in the measurement with the smallest number of significant figures.
***** Perform the following calculations and express the answer in the proper number of significant figures:
(12.257) x (1.162)
(5.61) x (7.891)
[(0.871) x (0.23)] ÷ (5.871)
***** Perform the following calculations and express the answer in the correct number of significant figures.
37.4 + 2.7 + 0.0015
256.3 – 137 + 2 + 10.11
129 ÷ 29.2
[(257) x (3.1)] ÷ (547)
[(12.4) x (7.943)] + .0064
[(246.83) ÷ (26.3)] – 1.349
Scientific Notation
1. Sometimes known as exponential notation.
2. This system helps us avoid the uncertainty of whether zeros at the end of a number are significant.
3. The exponent tells us how many decimal places to move the decimal point. The sign (+) or (-) tells us whether to move the decimal point to the left or the right.
4. Scientific notation is a method for making very large or very small numbers more compact and easier to write.
5. It expresses a number as a ______of a number between ______and the appropriate ______.
*****
6. When the decimal point is moved to the ______, the power of ten is ______.
*****
7. When the decimal point is moved ______, the power of ten is ______.
***** Express the following numbers to three significant figures in scientific notation:
3,500,0000.00134
0.000554003
10,300
8. To convert a number expressed in scientific notation into its normal expanded form simply move the decimal point the appropriate number of spaces in the direction indicated by the sign on the power of ten.
***** Express the following numbers in their normal expanded form.
2.38 x 105
1.5 x 10-3
9. To add or subtract numbers expressed in scientific notation, the exponents must be the same:
10. When multiplying numbers expressed in scientific notation, carry out the operation and then add the exponents together.
11. When dividing, carry out the operation and then subtract the exponent in the denominator from the exponent in the numerator.
12. When raising a number expressed in scientific notation to a power, carry out the operation, then multiply the exponent by the power.
Standard Units
1. In 1960, scientists adopted a part of the metric system to use as the standard scientific system of measurement units. This is called the “Systeme Internationale” or SI.
2. There are seven basic units. These base units can be combined in various ways to describe nearly all physical measurements. They are:
QuantityUnitSymbol
Length
Mass
Time
Electric current
Thermodynamic
temperature
Amount of
substance
Luminous intensity
Prefixes
1. Any SI unit can be modified with prefixes to match the scale of the object being measured. Meters might be suitable for measuring a person’s height, but not the diameter of a living cell.
PrefixSymbolMeaningPower of Ten
2. The prefixes can be combined with various units to describe the size of a measurement.
***** Suggest appropriate SI units and prefixes to measuring the following objects:
- the length of your chemistry book
- the volume of a bathtub
- the mass of an eyelash
- the volume of an aluminum soda can
Derived Units – Volume
1. The seven base SI units cannot measure every observable property; therefore derived units are created by multiplying or dividing the seven base units in various ways.
2. The derived unit for volume is obtained by using length, width and height measured in meters:
3. We are more familiar with using the liter, L, as a volume unit.
4. More commonly we use the following units to measure volume:
***** Speed is calculated from length and time according to the following equation. What is the derived SI unit?
Speed = distance / time
Density (pp 142 - 146)
1. Density is an intensive property. It does not depend on the quantity of matter present.
2. Density represents a ratio of mass to volume.
3. One interpretation of density is that it is a measure of how tightly matter is packed together.
4. Because the density of a substance is the same for all size samples of that substance, density can be used as a means of identifying materials.
5. To calculate density, one uses the following equation
6. The units for density are usually:
***** Determine the density of a piece of iron whose mass is 31.2 g and volume is 4.00 mL.
***** Clover honey has a density of 0.498 g/mL. Determine the mass of a sample having a volume of 225 mL.
***** Determine the volume of a piece of copper whose mass is 10.5g. The density of copper is 8.94 g/mL.
***** To determine the density of ethyl alcohol, a student pipets a 5.00 mL sample into an empty flask whose mass is 15.246g. She finds that the mass of the flask and the ethyl alcohol is now 19.171g. Calculate the density of the ethyl alcohol.
***** A solid with an irregular shape and a mass of 12.65g is added to a graduated cylinder filled with water to the 29.7 mL mark. After the solid sinks to the bottom, the water level of the graduated cylinder is read to be 36.6 mL. Calculate the density of the solid.
DIMENSIONAL ANALYSIS (130 - 135)
- It is a logical approach to problem solving.
- This technique applies to simple unit conversion problems as well as more complex chemical equations and calculations.
- These are the steps:
- Analyze the problem to determine the nature of the answer and its units.
- Identify the factors that are necessary, either those given in the problem statement or known from previous work.
- First place the factors containing the DESIRED UNITS of the answer in the proper numerator and/or denominator.
- Systematically arrange the remaining factors such that all units cancel EXCEPT for the units of the answer.
- Multiply and divide any numerical coefficients present in the factors and quantities given to obtain a numerical answer to accompany the answer units.
- Analyze the factors and given quantities to determine the proper number of significant figures for the answer.
- Inspect the calculated numerical answer to determine if it a REASONABLE answer, that is, if the size of the answer makes sense.
***** A certain person is 172 cm tall. Express this height in decimeters.
***** Convert 1.2L to mL
***** Convert 0.43m to cm.
***** Convert 650g to kg.
***** Calculate the number of meters in 0.200 miles.
***** Convert 0.250 lbs to grams.
***** How long is a 5.0 K race in miles?
***** In a certain part of the country, there is an average of 710 people per square mile and 0.72 telephones per person. What is the average number of telephones in an area of 5.0 km2?
ACCURACY AND PRECISION
- ______refers to how close a measured value is to an accepted value.
2. ______refers to how close a series of measurements are to one another.
3. Precise measurements may not be accurate.
4. Percent error is a way to evaluate the accuracy of experimental data:
***** The accepted value for the density of copper is 8.96 g/mL. Calculate the percent error for each of the following measurements:
a. 8.86 g/mL
b. 8.92 g/mL
c. 9.00 g/mL
- 8.98 g/mL
REPRESENTING DATA
Graphing
1. A graph is a visual display of data.
2. A circle graph (pie chart) is useful for showing parts of a fixed whole.
3. A bar graph is often used to show how a quantity varies with factors such as time, location, or temperature.
4. The quantity being measured, the ______variable, is plotted on the vertical axis (y-axis).
5. The ______variable is plotted on the horizontal axis (x-axis).
6. Line graphs represent the intersection of data for two variables. The independent variable is plotted on the x-axis and is the variable that a scientist deliberately changes during an experiment.
7. If the best-fit line is straight, there is a linear relationship between the variables and the variables are ______related.
8. A positive slope indicates that the dependent variable ______as the independent variable increases.
9. A negative slope indicates that the dependent variable ______as the independent variable increases.
METRIC CONVERSION INFORMATION
1 kilo _____ = 1000 _____
1 hecto _____ = 100 _____
1 deca _____ = 10 _____
1 kilo _____ = 10 hecto _____
1 kilo _____ = 100 deca _____
1 _____ = 10 deci _____
1 _____ = 100 centi _____
1 _____ = 1000 milli _____
1 deci _____ = 10 centi _____
1 deci _____ = 100 milli _____
1 centi _____ = 10 milli _____
kilo / hecto / deca / BASIC UNIT / deci / centi / milli(k) / (h) / (da) / gram (g) / (d) / (c) / (m)
1000 / 100 / 10 / liter (L) / .1 / .01 / .001
103 / 102 / 101 / meter (m) / 10-1 / 10-2 / 10-3
OVER