Download Chapter 2: Measurements and Calculations

Standards:
I & E: 1. f. Distinguish between hypothesis and theory as scientific terms.
1. g. Recognize the usefulness and limitations of models and theories as scientific representations of reality.
Objectives
Describe the purpose of the scientific method and the differences between hypotheses, theories and models.
Distinguish between qualitative and quantitative observations.
Name and use SI units for length, mass, time, volume, and density.
Perform density calculations.
Distinguish between accuracy and precision. Perform mathematical operations involving significant figures.
Convert measurements into scientific notation.
Chapter 2: Measurements and Calculations
Ch 2.1: The Scientific Method
The scientific method is a way to solve a scientific problem. It is an approach to a solution (using mostly
common sense.)
Example: Your flashlight doesn’t work. (Not necessarily a “scientific problem.”)
Steps to the Scientific Method
(1) Make observations-- Use your 5 senses to gather information.
(2) Propose a hypothesis-- Make an “educated guess” for what is happening.
(3) Perform experiments-- This tests your hypothesis. Many experiments are sometimes needed to test a
hypothesis. The same experiment must give similar results if the experiment is to be reliable.
(4) Make a theory-- This should explain the results of your experiments. Theories may change or be rejected
over time because of results from new experiments.
Models: are a part of theory that is an explanation of how phenomena occur and how data or events are related.
Qualitative Data: non-numerical data (ex. Green car)
Quantitative Data: numerical data (ex. 12 cars)
Ch 2.2 Measurement – Movie Clip 12:40 - 15:00
Every measurement must have a unit = 61.2 kilograms
SI Units
1795, French scientists adopted a system of standard units called the metric system; a committee of scientists
met to update the system and the revised system is called Le Système International d’Unitès, or SI units.
Base Units
There are 7 base units in SI.
A Base unit is a defined unit in a system of measurement that is based on an object
SI Base Units
Length (l)
Meter (m)
Mass (m)
Kilogram (kg)
Time (t)
Second (s)
Temperature (T)
Kelvin (K) and Celsius (°C)
Amount of Substance (n)
Mole (mol)
Electric Current (I)
Ampere (A)
Luminous Intensity (Iv)
Candela (cd)
Metric System
Prefixes Used with SI Units
Prefix
kilo
hecto
deca
Symbol
k
h
da
deci
centi
milli
micro
nano
pico
d
c
m

n
p
Exponential Factor
103
102
101
100
10-1
10-2
10-3
10-6
10-9
10-12
Example
kilogram(kg)
hectogram (hg)
decagram (dag)
gram (g)
decigram (dg)
centigram (cg)
milligram (mg)
microgram (g)
nanogram (ng)
picogram (pg)
An easy way to move within the metric system is by moving the decimal point one place for
each “step” desired
Example: change meters to centimeters
Use Prefixes!!!
Conversions
Kilo
1000
To convert to a smaller unit,
move decimal point to the right
or multiply.
Hecto
100
Deka
10
Basic
Unit
To convert to a bigger unit,
move decimal point to the left
or divide.
Deci
10
Centi
100
Milli
1000
400000 centimeters = _________kilometers
500 kilometers = __________meters
Summary
Base units in the metric system are meter, liter, gram, etc.
Metric system is based on powers of 10
For conversions within the metric system, each “step” is 1 decimal place to the right
or left.
Derived Units
A unit that is defined by a combination of base units is called a derived unit.
Examples are Area, Volume, Density, Molar Mass, Molar Volume, and Energy.
The two derived units we will be working with in this chapter are volume and density.
Volume
Volume is the space occupied by an object.
The derived unit for volume is the cubic centimeter (cm3); used for solid objects.
Liters are used to measure the amount of liquid in a container.
For the smaller quantities of liquids, volume is measured in milliliters (mL).
1 mL = 1 cm3
Density
Density is a ratio that compares the mass of an object to its volume
The units for density:
grams per cubic centimeter(g/cm3) for solids
grams per milliliter (g/mL) for liquids
The density of an object will determine if it will float or sink in another phase. If an object floats, it
is less dense than the other substance. If it sinks, it is more dense.
The density of water is 1.0 g/mL, and air has a density of 0.00129 g/mL.
Be able to rearrange density equation to solve for density, mass, and volume
D = m/V
V = m/D
m=DxV
Example 1
A sample of aluminum metal has a mass of 8.4 g. The volume of the sample is 3.1 cm3. Calculate the density of
aluminum. Answer: 2.7 g/cm3
Conversion Factor:
A ratio of equivalent values used to express the same quantity in different units.
A conversion factor is always equal to 1.
Because a quantity does not change when it is multiplied or divided by 1, conversion factors change
the units of a quantity without changing its value.
This is also known as dimensional analysis and it will be used a lot throughout the year. The key to
doing dimensional analysis is making sure that your units cancel out!
Example 2
Express a mass of 5.712 grams in milligrams and kilograms
Grams to milligrams
Grams to kilograms
1 g = 1000 mg
1 kg = 1000 g
Answer: 5712 mg 0.005712 kg
Temperature
The temperature of an object is a measure of how hot or cold the object is relative to other objects.
Temperature scales - scientists use two temperature scales
Celsius (oC) scale was devised by Anders Celsius
He used temperatures at which water freezes and boils to establish his scale
Freezing point of water – 0 oC
Boiling point of water – 100 oC
The Kelvin (K) scale was devised by William Thomson and is the SI base unit of temperature
On the Kelvin scale water freezes at 273 K and boils at 373 K
°C + 273 = K
K – 273 = °C
Ch 2.3 Using Scientific Measurements – Movie Clip 15:00 – 19:45 and 19:45 – 23:15
A digit that must be estimated is called uncertain. A measurement always has some degree of uncertainty.
Precision and Accuracy
Accuracy refers to the agreement of a particular value with the true value.
Precision refers to the degree of agreement among several measurements made in the same manner.
Percent Error
Experimental values are measured during an experiment
Accepted value = true value
Error = (Experimental value - accepted value)
When you calculate percent error, you ignore plus and minus signs
The lower the % error means lab technique is good.
Percent Error = | Experimental Value – Accepted Value | x 100
Accepted Value
Significant Figures
Scientist indicate the precision of measurements by the number of digits they report - Significant figures
A value of 3.52 g is more precise than a value of 3.5 g.
1. Non-Zero Rule: All digits 1-9 are significant.
2. Straddle Rule: Zeros between two significant figures are significant.
3. Righty-Righty Rule: Zeros to the right of a decimal point AND anywhere to the right of a significant
figure are significant.
4. Bar Rule: Any zeros that have a bar placed over them are significant. (Only use this for zeros that are
not already significant: Rules 2 & 3.)
5. Counting Rule: Any time the measurement is determined by simply counting the number of objects, the
value has an infinite number of significant figures.
Sig Fig Practice #1
Rules for Significant Figures in Mathematical Operations
Addition and Subtraction: use the least number of places after the decimal between all the numbers you are
adding or subtracting.
6.8 + 11.934 = 18.734  18.7 (3 sig figs)
Sig Fig Practice #2
Rules for Significant Figures in Mathematical Operations
Multiplication and Division: use the least number of sig figs between the numbers you are measuring.
6.38 x 2.0 = 12.76  13 (2 sig figs)
Sig Fig Practice #3
Scientific Notation
Scientific notation is a way of representing really large or small numbers using powers of 10.
*Examples: 5,203,000,000,000 miles = 5.203 x 1012 miles
0.000 000 042 mm = 4.2 x 10−8 mm
Steps for Writing Numbers in Scientific Notation
1. Write down all the sig. figs.
2. Put the decimal point between the first and second digit.
3. Write “x 10”
4. Count how many places the decimal point has moved from its original location. This will be the
exponent...either + or −.
5. If the original # was greater than 1, the exponent is +, and if the original # was less than 1, the exponent is ....(In other words, large numbers have + exponents, and small numbers have - exponents.
PERFORMING CALCULATIONS IN SCIENTIFIC NOTATION
Addition and Subtraction
1. IF the exponents are the same, we simply add the numbers in front and bring the exponent down unchanged.
2. The same holds true for subtraction in scientific notation.
3. If the exponents are NOT the same, we must move a decimal to make them the same.
4. Move the decimal on the smaller number!
Multiplying and Dividing
1. Multiply the front factors first.
2. Then add the exponents.
3. Make sure that only one number is in front of the decimal at the end of the problem.
4. Divide the front factors first.
5. Then subtract the exponents.
Graphing
 Using data to create a graph can help to reveal a pattern if one exists.
 A graph is a visual display of data.
Circle graphs
 A circle graph is sometimes called a pie chart because it is divided into wedges like a pie or pizza.
 The parts are usually labeled as percents with the circle as a whole representing 100%.
Bar graph
 A bar graph often is used to show how a quantity varies with factors such as time, location, or temperature.
 In those cases, the quantity being measured appears on the vertical axis (y-axis).
 The independent variable appears on the horizontal axis (x-axis).
 The heights of the bars show how the quantity varies.
Line Graphs
 In chemistry, most graphs that you create and interpret will be line graphs.
 The points on a line graph represent the intersection of data for two variables.
 Dependent variable - plotted on the y-axis.
 Independent variable – plotted on the x-axis.
 This variable is the one that the scientist deliberately changes during an experiment.
 Sometimes points are scattered, the line cannot pass through all the data points.
 The line must be drawn so that about as many points fall above the line as fall below it.
 This line is called a best fit line.
 If the best fit line is straight, there is a linear relationship between the variables and the variables are directly
related.
 This relationship can be further described by the steepness, or slope, of the line.
 If the line rises to the right, the slope is positive.
 A positive slope indicates that the dependent variable increases as the independent variable increases.
 These are directly related.
 If the line sinks to the right, the slope is negative.
 A negative slope indicates that the dependent variable decreases as the independent variable increases.
These are inversely related.
 The slope is the change in y divided by the change in x.