Scientific Method

• Observation

» Qualitative vs. quantitative data

• Hypothesis

• Experimentation

» Control - standard used for comparison

» Independent variable - what the researcher changes

» Dependent variable – measured result

• Conclusion

• Theory – supported by many experiments

What is Scientific Notation?

• Scientific notation is a way of expressing really big numbers or really small numbers.

• It is most often used in “scientific” calculations where the analysis must be very precise.

• For very large and very small numbers, scientific notation is more concise.

Scientific notation consists of two parts:

• A number between 1 and 10

• A power of 10

N x 1 0 x

Measurements

Number followed by a Unit from a measuring device

SI Units (Le Système international d'unités) – based on the metric system

Time second (s)

Length meter (m)

Mass kilogram (kg)

Temperature Kelvin (K)

Amount of a substance Mole (mol)

Metric Prefixes

Conversion factors

• Fractions in which the numerator and denominator are EQUAL quantities expressed in different units

• Dimensional Analysis (Factor-label method)

• A way of solving problems using conversion factors

• By using dimensional analysis the UNITS ensure that you have the conversion factor in the proper arrangement

Significant Figures

The numbers reported in a measurement are limited by the measuring tool

Significant figures in a measurement include all; the known digits plus one estimated digit

Which of the two clocks below has the

potential to be the most accurate? Why?

Comparing Rulers

Zero as a Measured Number

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

What is the length of the line?

First digit 5.?? cm

Second digit 5.0? cm

Last (estimated) digit is 5.00 cm

Reading a Meterstick

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

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

Second digit (known) = 0.7 2.7? cm

Third digit (estimated) between 0.05- 0.07

Length reported = 2.75 cm

or 2.74 cm

or 2.76 cm

Rules for Significant Figures adapted from Russo's Reliable Rules for Significant Figures

1. All non-zero digits are significant

2. Zeroes between non-zero digits are significant

3. In measurements containing an expressed decimal,

zeros to the right of NON-ZERO digits are significant.

“Atlantic - Pacific Rule”

Count from the ocean towards the coast starting with the first

nonzero digit, and include all the digits that follow.

Significant Numbers in Calculations

A calculated answer cannot be more precise than the measuring tool.

A calculated answer must match the least precise measurement.

Significant figures are needed for final answers from

1) adding or subtracting

2) multiplying or dividing

Adding and Subtracting

The answer has the same number of decimal places as the measurement with the fewest decimal places.

Practice:

a) 2.45 cm + 6.382 cm + 5.8 cm

b) 18.92 mL - 10.42 mL

c) 22.100 g -13 g + 2.93g

14.6 cm

8.50 mL

12 g

Multiplying and Dividing

Round (or add zeros) to the calculated answer until you have the same number of significant figures as the measurement with the fewest significant figures.

Practice:

a) 4.20 m x 3.21 m x 0.16 m

b) 100.35 g / 90.2 mL

c) (3.28 x 10-5 km) / (4 x 102 s)

2.2 m3

1.11 g/mL

8 x 10-8 km/s

Temperature Scales

• Fahrenheit

• Celsius

• Kelvin

Anders Celsius

1701-1744

Lord Kelvin

(William Thomson)

1824-1907

Temperature Scales

Notice that 1 kelvin = 1 degree Celsius

Boiling point

of water

Freezing point

of water

Celsius

100 ˚C

0 ˚C

100˚C

Kelvin

373 K

273 K

100 K

Calculations Using Temperature

• Generally require temp’s in Kelvin

•K = ˚C + 273

• Body temp = 37 ˚C + 273 = 310 K

• Liquid nitrogen = -196 ˚C + 273 = 77 K

Temperature Demonstration

1. Obtain three cups of water. One with hot water, one

with ice cold water and one with room temperature

water.

2. Place one hand in the hot water and the other in the

cold water at the same time. Keep hands in the water

for 30-60 minutes.

3. Simultaneously, remove both hands and place them

both in the cup of room temperature water.

What did you observe? Why do you think this happened?

Derived Units – a combination of 2 or more base units

• Area (length x length)

• Speed (length per time)

• V olume (length x length x length)

• Density (mass per volume)

DENSITY

Density mass (g)

volume (cm3)

13.6 g/cm3 21.5 g/cm3

Aluminum

2.7 g/cm3

Platinum Mercury

Learning Check

Osmium is a very dense metal. What is its

density in g/cm3 if 50.00 g of the metal occupies

a volume of 2.22cm3?

1) 2.25 g/cm3

2) 22.5 g/cm3

3) 111 g/cm3

Solution

2) Placing the mass and volume of the osmium metal into the density setup, we obtain

D = mass = 50.00 g =

volume 2.22 cm3

= 22.522522 g/cm3 = 22.5 g/cm3

Volume Displacement

A solid displaces a matching volume of water when the solid is placed in water.

33 mL

25 mL

Learning Check

What is the density (g/cm3) of 48 g of a metal if the metal raises the level of water in a graduated cylinder from 25 mL to 33 mL?

1) 0.2 g/ cm3 2) 6 g/cm3 3) 252 g/cm3

33 mL

25 mL

Solution

Volume (mL) of water displaced

= 33 mL - 25 mL = 8 mL

Volume of metal (cm3)

= 8 mL x 1 cm3 = 8 cm3

1 mL Density of metal =

mass = 48 g = 6 g/cm3

volume 8 cm3

The answer is: 2) 6 g/cm3

Three targets with three arrows each to shoot.

Can you hit the bull's-eye?

Both accurate and precise

Precise but not accurate

Neither accurate nor precise

How do they compare?

Can you define accuracy and precision?

How can someone show the accurate the

measurement?

Calculation of percent error

(Value accepted - Value experimental)

Value accepted

x 100 Percent Error (%) =

Graphing Data

1. Bar graphs

2. Circle graphs

3. Line graphs

Directly proportional

Inverse proportional