The Basics Chapter 1. Mathematics- The Language of Science Ideas and values are expressed...

The Basics

Chapter 1

Mathematics- The Language of Science

• Ideas and values are expressed mathematically to give clarity of meaning and easier to prove/disprove

Scientific Notation and Significant Figures

• Method for writing values and keep only the digits required.

• Rules for Writing in Significant Figures– 1. Every nonzero digit in a recorded measurement is significant. 24.7 m,

0.743 m and 714 m all have three significant figures. – 2. Zeroes appearing between nonzero digits are significant. The

measurements 7003 m, 40.79 m, and 1.503 m all have four significant figures.

– 3. Zeroes in front of (before) all nonzero digits are merely placeholders; they are not significant. 0.0000099 only has two significant figures.

– 4. Zeroes at the end of the number if a decimal point is present and also zeroes to the right of the decimal are significant. The measurements 1241.20 m, 210.100 m and 5600.00 all have six significant digits.

– 5. Zeroes at the end of a measurement and to the left of an omitted decimal point are ambiguous. They are not significant if they are only place holders: 6,000,000 live in New York—the zeroes are just to represent the magnitude of how many people are in N.Y. But the zeroes can be significant if they are the result of precise measurements. A vinculum over the least significant zero is often used.

Convert each of the following into scientific notation. 

1. 727   2. 1720003. 0.000984  4. 200.0 x 102    5. 0.014 x 102   

Give the number of significant figures in each of the  following.

6.  1.05 g  7.  0.0003040 mm 8.  29000 + 10 ft  9.  0.90 x 1045 L 

Exponential (Scientific) Notation : Calculations

• Rule for Multiplication - When you multiply numbers with scientific notation, multiply the coefficients together and add the exponents. The base will remain 10.

• Rule for Division - When dividing with scientific notation, divide the coefficients and subtract the exponents. The base will remain 10.

Exponential (Scientific) Notation : Calculations

• Rule for Addition and Subtraction - when adding or subtracting in scientific notation, you must express the numbers as the same power of 10. This will often involve changing the decimal place of the coefficient.

SI Units

• In science we have standardized units for measuring and recording information.

• Time- second• Length- meter• Temperature- Kelvin• Mass- kilogram

*please note that SI units do not have to be base units. (look at mass)

**derived units are those which are created from more than one unit. (speed of an object mph)

Unit Prefixes

• Mega- 1 x 106 1000000• Kilo- 1 x 103 1000• Hecto- 1 x 102 100• Deca- 1 x 101 10• Base- 1 x 100 1• Deci- 1 x 10-1 .1• Centi- 1 x 10-2 .01• Milli- 1 x 10-3 .001• Micro- 1 x 10-6 .000001• Nano- 1 x 10-9 .000000001• Pico- 1 x 10-12 .000000000001

Practice:

Convert the following values. Write the answer in scientific notation:

• 2000 kg to g• 300 cm to mm• 15 s to ms1. 1348 μm to hm2. 8735 ps to Ms

The Basic Science

• Science used to be called ‘natural philosophy’– It is the study of unanswered questions

• There are two broad categories of science:– Biological Science- biology, zoology, botany,

…– Physical Science- physics, chemistry,

geology, astronomy, ….

• Physics is the basic science. It is the study of motion and forces

• Chemistry is more complex. It is the study of atoms, how and why they combine and react.

• Biology is the study of molecules and compounds, how they interact with life and the environment

Why study physics?

• Most modern technology came form physics• Most branches of science contain principles

obtained from physics• A knowledge of physics is essential for

understanding music, art, and literature• Also….physics hones thinking skills, college

success is increased by taking challenging classes (physics), and there is a strong job market for physicists

Scientific Method

• Let’s list the steps of the scientific method: – Recognize a problem– Make an observation– Formulate a hypothesis– Conduct an experiment– Collect data– Analyze data– Make a conclusion based on the data

• Okay….so we just completed all the steps of the scientific method….what is next?

• What if your hypothesis is not supported?

• What if your hypothesis is supported?

Hypothesis

• A hypothesis must meet two criteria: – Testable- able to be tested– Null- proven false

Practice

Identify if each of the following statement is a hypothesis and if not, why.

1. Pepperoni is the best pizza topping. 2. Our universe is surrounded by another, larger

universe with which we can have no contact. 3. There are other inhabited planets in the

universe. 4. Any two objects dropped from the same height

will hit the ground at the same time, neglecting air resistance.

Parts of an Experiment

• Variables- factors that change or are changed in an experiment– Independent variable- what is changed or

manipulated– Dependent variable- what changes because of the

independent variable

• Constant- variables in an experiment that is kept constant for all trials

• Control- the trial that you control to compare results to (does not receive the independent variable treatment)

Practice

Identify the variables in this experiment:

Students of different ages were given a jigsaw puzzle to put together. They were timed to see how long it took to finish the puzzle.

Practice

Identify the variables in this experiment:

The temperature was measure at different depths of water in a pond.

Practice

Identify the variables in this experiment:

The higher the temperature of water, the faster the egg will boil.

The Scientific Attitude

• Fact is the close agreement by competent observers who make a series of observations of the same phenomenon

• Law/principle is a hypothesis that has been tested over and over again without contradiction

• Theory is a large body of information that encompasses well-tested and verified hypothesis about certain aspects of the natural world

• Science is always evolving and changing as new information is discovered. – Is this a strength of weakness of science?

Science, Technology, and Science

• Science is a method of answering theoretical questions

• Technology is a method of solving practical problems

Graphing Activity

• Please work with the members at your lab table. In your notes, identify: – The different types of graphs and what they

are used for. – The parts needed in a graph. – You have 5 minutes.

– Go!!!

Graphing Notes

0

2

4

6

8

10

12

0 2 4 6 8 10 12

De

pe

nd

en

t Va

ria

ble

Da

ta L

ab

ele

(u

nit

s)

Independent Variable Data Labele (units)

Title

Series1

Best Fit or

Trendline

Data Points

Scale

Extra Notes

• Accuracy vs Precision– Accuracy is how well the results agree with

the standard (hitting the bulls eye)– Precision degree of exactness of the

measurements (all the arrows hitting in the same area)

• Linear Relationships- directly proportional values.

• Nonlinear relationships- indirectly proportional

Activity• With your partner- create a lab activity to

measure a paper air plane flight distance.

• Create a paper air plane.

• Write a procedure to test the distance.

• Make 1 modification and repeat the procedure.

• Identify the independent variable, dependent variable, constants, and control of the activity.

*each person does this on his/her paper