Basic Science Information

•Exponent Rules & Scientific Notation•Units and the M-K-S System•Dimensional Analysis•Significant Figures•Variables and the Scientific Method

By Vincent Sapone

What is Science?

• Study of the world around us.

• Uses observation and experimentation, logic, reason.

• Makes predictions, is testable and is generally repeatable.

Types of Science

• There are a ton of different branches to science:

• If it stinks its probably Chemistry.• If its Slimy its probably Biology.• If its Broken its probably Physics.• If you can’t lift it its probably geology.• If you can’t predict its probably meteorology.• If you can’t get there its probably Astronomy• If it makes no sense its quantum mechanics or relativity.• If it assumes cows are spherical its probably Mathematics.

Scientific Notation

Exponential Notation is useful to science because

1. Very small numbers are used.2. Very large numbers are used3. It is also easier to solve large numbers adding exponents.4. It uses factors of ten and accommodates metric system.

• Example: Rest Mass of Electron = 0.000000000000000000000000000000911 kg

• Compare that to 9.11x10^-31

Exponential Numbers: Powers of 10

• Any Number written as A x 10B • A is usually between 1 and 10• B is usually an integer.

• Example I: 93,450,000 9.345 x 107 • 7th power means move the decimal place right 7 places.

• Example II: 0.0001728 1.728 x 10-4

• The - 4th power means to move the decimal place to the left 4 places.

Exponent Rules• Rule 1

• Example

Exponent Rules• Rule 2

• Example

Exponent Rules• Rule 3

• Proof from Rule 1:

Exponent Rules• Rule 4

• Example

Why Scientific Notation is Easier

Example: 6,350,000,000 x 424,000,000 = 6.35 x10^9 x 4.24x10^8.

• Using rule one we add the exponents (8+9) and multiply the leading numbers (6.35 x 4.24). This is an easier calculation to perform.

• Answer = (6.35 x 4.24) x 10^17

Scientific Notation

• Example Problems• Homework Assignment

Units, Conversions & M-K-S SystemSystem Length Mass Time

MKS Meter (m) Kilogram (kg) Second (s)

CGS Centimeter (cm) Gram (g) Second (s)

British Foot (ft) Pound (lb) Second (s)

• In science we use the MKS system

•The mks system is preferred because its units are divisible by 10.

Metric Prefixes

• yotta- (Y) 1024 1 septillion• zetta- (Z) 1021 1 sextillion• exa- (E) 1018 1 quintillion• peta- (P) 1015 1 quadrillion• tera- (T) 1012 1 trillion• giga- (G) 109 1 billion• mega- (M) 106 1 million• kilo- (k) 103 1 thousand• hecto- (h) 102 1 hundred• deka- (da) 10 1 ten• deci- (d) 10-1 1 tenth• centi- (c) 10-2 1 hundredth• milli- (m) 10-3 1 thousandth• micro- (µ) 10-6 1 millionth• nano- (n) 10-9 1 billionth• pico- (p) 10-12 1 trillionth• femto- (f) 10-15 1 quadrillionth• atto- (a) 10-18 1 quintillionth• zepto- (z) 10-21 1 sextillionth• yocto- (y) 10-24 1 septillionth

Conversion is EasierThree Yards into Feet

• 3 goes to 36• We have a new number.

Three Meters into Centimeters

• 3 goes to 300• Decimal moves two places

The MKS jut moves the decimal to the right two places. Much more convenient especially when dealing with the very large and small numbers of science.

Universal System• It is convenient to use one system so that we

understand the numbers.

• If I said tomorrows High will be 283 kelvins what does that tell you?

• Likewise, if I said it will be 10 degrees C?

• Also if I said John has a speed of 7 what does that tell you? You need to ask 7 what?

Special Units:

• Example: Newton (kg m/s^2) [F=MA]

• Example: Joule (kg m^2/s^2 ) [KE = (1/2)mv^2

• Do KE and PE have the same Units? (mgh and 1/2mv^2).

Dimensional Analysis & Unit Conversion

• We often need to convert between units in science.

• Suppose a truck on the highway was traveling at 65 km per hour and I wanted to know its speed in miles per hour or meters per second.

Problem 1 (Level I)

• Problem 1: Convert 10 miles into centimeters.

• Solution: First we must find a Conversion Factor and set it up so the units cancel. A conversion factor is essentially equal to One.

• Conversion Factor: 1 Mile = 1.609 Kilometers so we first convert the 10 miles into kilometers:

•1.609 kilometers = 1 mile is the conversion factor•The units of miles cancel in division.•Now we convert kilometers to meters and then meters to centimeters

Problem 2 (level II)

• Problem 2: Convert 60 milers per hour into meters per second.

• Solution: We must convert both miles into meters and hours into seconds.

• Conversion Factor: 1 Mile = 1.609 Kilometers so we first convert the 60 miles into kilometers:

Problem 3 (level II)• Problem 3: Determine the units of the gravitational

constant

Solution: the left hand of an equation must always have the same unit

Gravitational Constant = 6.67 x 10^-11 ((m^3)/ (s^2* kg)

Problem 4 Level (II)• Problem: Show that G also = (N*M) / KG^2• Solution: Find the units for Newtons the same way we did for the

Gravitational Constant.

Significant Figures• Important b/c of measured vs. known numbers. • E.g., the length of a desk versus the # of desks in a room.• Think of some other examples…

• There are ALWAYS errors in measurements.

• Sigfigs tell us that the result of any experiment cannot be more accurate than the data used.

• Sigfig’s let readers know the accuracy you used in an experiment.

SigFig Example

• Suppose I ask you to measure the length of a desk with a meter stick.

• You tell me it is 0.756563874 meters.

• Should I applaud you for your high level of precision and accuracy?

Significant Figures

• Did you really read the meter stick with your naked eye to a hundred millionth of a meter?

• Your naked eye is not that precise and your value is suspect.

Reading a Meter Stick• A meter sticks’ smallest division is usually cm.

• The best we can do is estimate one doubtful figure after centimeters.

• An object is between 45 and 46 centimeters and you estimate it at 45.6 cm.

• 45 can be considered a known or number while the .6 is a measured or doubtful one.

• The Significant Figures of a measured value include those numbers directly readable from a measuring device plus one doubtful figure.

• Calculators make errors since they assume all numbers are known.

Measured Numbers

When you use a measuring tool is used to determine a quantity such as your height or weight, the numbers you obtain are called measured numbers.

Reading a Meterstick

. l2. . . . I . . . . I3 . . . .I . . . . I4. . cm

First digit (known) = 2 2.?? cm

Second digit (known) = 0.6 2.6? cm

Third digit (estimated) between 0.05- 0.07

Length reported = 2.65 cm

or 2.66 cm

or 2.67 cm

Known + Estimated Digits

Known digits 2 and 6 are 100% certain

The third digit 5 is estimated (uncertain)

In the reported length, all three digits

(2.65 cm) are significant including the estimated

one

Learning Check

. l8. . . . I . . . . I9. . . .I . . . . I10. . cm

What is the length of the line?

How does your answer compare with your neighbor’s answer? Why or why not?

Solution

. l8. . . . I . . . . I9. . . . I . . . . I10. . cmEstimate to the hundreth’s place (0.01 cm)

The estimated digit may be slightly different.

Learning Check

l5. . . . I . . . . I6. . . . I . . . . I7. . cm

What is the length of the line?1) 6.2 cm 2) 6.199 cm3) 6.18 cm

Zero as a Measured Number

. l3. . . . I . . . . I4 . . . . I . . . . I5. . cm

What is the length of the line?

First digit 4.?? cmSecond digit 4.5? cmLast (estimated) digit is 4.50 cm

Exact Numbers

Obtained when you count objects2 soccer balls1 watch4 pizzas

Obtained from a defined relationship1 foot = 12 inches1 meters = 100 cm

Not obtained with measuring tools

Learning Check

A. Exact numbers are obtained by 1. measuring

2. counting3. definition

B. Measured numbers are obtained by 1. measuring

2. counting3. definition

Solution

A. Exact numbers are obtained by 2. counting

3. definition

B. Measured numbers are obtained by 1. Using a measuring tool

Learning Check

Classify each of the following as an exact (1) or a measured (2) number.

A.___Gold melts at 1064°C

B.___1 yard = 3 feet

C.___A red blood cell with diameter 6 x 10-4 cm

D.___There were 6 hats on the shelf

E.___A can of soda contains 355 mL of soda

Solution

Classify each of the following as an exact (1) or a measured(2) number. Give reason.

A. 2 Requires a thermometer(measuring tool)

B. 1 From a definition in U.S. system

C. 2 Need measuring tool to determine

D. 1 Counted the hats

E. 2 Measured

Significant Figures

1. All non-zero numbers are always significant (e.g. 123456789)2. All zeroes between non-zero numbers are significant (7007). 3. All zeroes both to the right of a decimal point and at the end of a

number are significant. (.007 has 1 sf and 700 = 1 but 7.00 = 3)4. All zeroes left of a decimal point in a number > 10 are significant.

(700.4 = 4 sf)

To check #3 and #4 write the number in scientific notation. If you can get rid of the zeroes they are not significant.

SigFig examples…

Sigfig Products and Quotients

• When multiplying or dividing, the answer cannot have more significant figures than the term with the least number of significant figures.

• For example 25.2 x 2.543 = 64.0836 in a calculator.

• The answer is 64.1 however.

Sigfig Addition and Subtraction

• In addition and subtraction the number of decimal places is what is important.

• The answer cannot have more decimal places than the term with the least number.

• 25 + 1 = 26 but • 25.331 + 1.33 = 26.66 not 26.661

Sigfigs’s

• Do sample problems on the board• Assign Homework Problems

Scientific Method

• Hypothesis is an educated guess to solve a problem.• Theory is a better hypothesis that is backed by physical

data, etc.

• A Scientific Model is a combination of Theories • Stellar Evolution combines theories and laws pertinent

to Nuclear Physics, Gas laws, thermodynamics and Gravity into a cohesive whole.

SCIENTIFIC METHODControl Variable– stays constant in an experiment Independent Variable – manipulated by observer Dependent Variable – effects of the independent variable are measured

Step 1. Observe / experiment (gather data).

Step 2. Hypothesize (explain).

Step 3. Test the hypothesis by prediction.

Step 4. Modify or reject the hypothesis.

Occam’s Razor: The explanation that makes the fewest assumptions is the preferred one.

GENERALIZE to many situations

Variable Identification Ex. 1Can blueberries slow down aging?

• A study indicates that antioxidants found in blueberries may slow down the process of aging. In this study, 19-month old rats (equivalent to 60-year old humans) were fed either their standard diet or a diet supplemented by either blueberry, strawberry, or spinach powder. After eight weeks, the rats were given memory and motor tests. Although all supplemented rats showed improvement, those supplemented with blueberry powder showed the most notable improvement.

• What is the independent variable? (diet: blueberries or no blueberries)• What are the dependent variables? (memory test and motor skills test)• What are the Control variables? (same rates, same equipment used in

tests, et al)

Variable Identification Ex. 2

Does beta-carotene protect against cancer?

• Beta-carotene supplements have been thought to protect against cancer. However, a study published in the Journal of the National Cancer Institute suggests this is false. The study was conducted with 39,000 women aged 45 and up. These women were randomly assigned to receive a beta-carotene supplement or a placebo, and their health was studied over their lifetime. Cancer rates for women taking the beta-carotene supplement did not differ systematically from the cancer rates of those women taking the placebo.

• Independent variable? (supplements, beta-carotene, placebo)• What are the dependent variables? (occurrence of cancer)• What are the Control variables? (same equipment used in

tests, et al)

Variable Identification Ex. 3

How bright is right?

• An automobile manufacturer wants to know how bright brake lights should be in order to minimize the time required for the driver of a following car to realize that the car in front is stopping and to hit the brakes.

• What is the independent variable? (brightness of brake light)• What is the dependent variable? (time to hit brake)• What are some control variables (same equipment, same driver, same

cars, the same lighting is used during the test)

Variable Identification Ex. 4

Class Activity!!

• We will now come up with something we want to test. It can be anything, e.g. how does temperature impact how high a basketball bounces. Once the issue and method are figured out we will label the following:

• What is the independent variable? • What is the dependent variable? • What are some control variables?