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Data Analysis

- Chapter 2

Units of Measurement

- Is a measurement useful without a unit?

SI Units

- The metric system is used worldwide.
- Long ago, inexact measurements were used. For

example - Boundaries wouldve been marked off by walking

counting the number of steps. - Time was measured with a sundial or an hourglass

filled with sand.

SI Units

- The metric system was adopted in 1795 by a group

of French scientists. - In 1960, an international committee of scientists

met to update the metric system. Called the SI

system (Systeme Internationale dUnites)

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 or event in the physical

world. - The base unit for
- Time is second electrical current is
- Length is meter amount of sub is
- Mass is kilogram luminosity is
- Temp is
- The prefixes used with SI units are (table 2-2)

Derived Units

- A derived unit is a unit that is defined by a

combination of base units. - Example speed is meters/second (m/s)
- Get out your calculators!

Volume

- Volume is the space occupied by an object.
- 1 L 1 dm3 1 mL 1 cm3
- You would use a graduated cylinder to measure the

volume of a liquid in the lab. - You would measure length x width x height to find

the volume of a regular solid. - How would you find the volume of an irregular

solid?

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Density

- Density of a ratio that compares the mass of an

object to its volume - Dm/v
- Ex 1 Calculate the density of a piece of aluminum

that has the mass of 13.5g a volume of 5.0cm3.

What is this substance?

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- Ex 2 Suppose a sample of aluminum (Al) is placed

in a graduated cylinder containing 10.5 mL of

water rises to 13.5 mL. What is the mass of the

aluminum sample? (Use the density from example 1)

Density

- Density of a substance is a property that doesnt

change, UNLESS altered by an outside substance. - Dwater at STP is 0.998 g/cm3
- Dwater at 4C is 1.00 g/cm3
- practice problems 1-3

- If we know the Density dimensions of a cube,

can we determine the mass of the cube? - If the Dair 0.00122 g/cm3, then what is the mass

of air in this room?

Temperature

- Temperature is the measure of how hot/cold an

object is relative to other objects. - Scales of temperature
- Celsius- derived by Anders Celsius used the

point at which water freezes boils to establish

his scale - Freezing point- 0 C
- Boiling point- 100 C

Temperature

- Kelvin (K)- derived by William Thomson, known as

Lord Kelvin - Kelvin is the SI base unit of temperature
- Conversion process of Celsius to Kelvin
- Add 273
- Conversion process of Kelvin to Celsius
- Subtract 273
- Ex.

- Practice problems 4-6
- 4. Convert 357C to Kelvin
- 5. Convert -39C to Kelvin
- 6. Convert 266 K to Celsius

Scientific Notation

- Scientific notation- expresses a number as a

number between 1 10 and then raised to a power,

or exponent. - When a number is more than one, the exponent is

positive. - If less than one, the exponent is negative.

Scientific Notation

- How do we convert data into Sci. Not. ?
- Move the decimal until you have a number between

1 10. - The exponent in the number of times you moved the

decimal. - Put unit with answer.

Scientific Notation

- Practice problems 1-8
- 700 m
- 38 000 m
- 4 500 000m
- 685 000 000 000 m

- 5. 0.0054 kg
- 6. 0.000 006 87 kg
- 7. 0.000 000 076 kg
- 8. 0.000 000 000 8 kg

Calculations with Sci Not.

- How do we add/subtract using Scientific Notation?
- Make sure exponents are the same.
- If the exponent is too large, decrease it move

the decimal that many times to the right. - If the exponent is too small, increase it move

the decimal that many places to the left.

Calculations with Sci Not.

- Ex. What is 2.70 x 107 15.6 x 106?
- practice problems 5-8

- 1.26x104 kg 2.5x103 kg
- 7.06x10-3 kg 1.2x10-4 kg
- 4.39x105 kg 2.8x104 kg
- 5.36x10-1 kg 7.40x10-2 kg

Calculations with Sci Not.

- How do we multiply/divide using sci. not.?
- Multiply/divide the factors(aka coefficients)

first. - Multiplication
- Add the exponents.
- Division
- Subtract the exponent of the denominator from the

exponent of the numerator.

Calculations with Sci Not.

- Ex.1 What is (2 x 103) x (3 x 102)
- Ex. 2 What is (9 x 108) / (3 x 10-4)
- practice problems 9-16.

- 9. (4x102 cm)x(1x108 cm)
- 10. (2x10-4 cm)x(3x102 cm)
- 11. (3x101 cm)x(3x10-2 cm)
- 12. (1x103 cm)x(5x10-1 cm)
- 13. (6x102 g)/(2x101 cm3)
- 14. (8x104 g)/( 4x101 cm3)
- 15. (9x105 g)/ (3x10-1 cm3)
- 16. (4x10-3 g)/(2x10-2 cm3)

Dimensional Analysis

- Dimensional analysis- method of problem-solving

that focuses on the units used to describe

matter often uses conversion factors. - Conversion factor- ratio of equivalent values

used to express the same quantity in different

units. - Ex 1 How many hours are in one year?

Conversion Factors

- Giga
- Mega
- Kilo
- Hecto
- Deca
- BASE
- Deci
- Centi
- Milli
- Micro
- Nano
- (Angstro)
- Pico

Dimensional Analysis

- Ex. 1 How many meters are in 48 km?
- Practice
- What conversion factor should be used for the

following conversion? - A. 360 s ? ms
- B. 4800 g ? kg
- C. 6800 cm ? m

Practice using dimensional analysis

- 4.5 L __________mL
- 0.095mg ____________cg
- 9500 mm ___________m
- 0.575 km ___________m
- 100 cm ___________mm

- Handout Unit Conversion

Conversion

- Ex. 2 What is the speed of 550 meters per second

in kilometers per minute?

Practice

- 6) How many seconds are there in 24.0 hours?
- 86,400 s
- 7) the density of gold is 19.3 g/mL. What is

golds density in decigrams per liter? - 193,000dg/L
- 8) A car is travelling 90. kilometers per hour.

What is the speed in miles per minute? (1 km0.62

mi) - 0.93 mi/min

Reliability

- How reliable are measurements?
- Accuracy Precision
- Accuracy- refers to how close a measured value is

to an accepted value. - Precision- refers to how close a series of

measurements are to one another.

Accuracy or precision

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Percent Error

- Percent error- ratio of an error to an accepted

value. - error accepted(book value) exp (you) x

100 accepted - error (error/accepted) x 100
- Ignore the negative sign, only the amount of

error matters.

Percent Error

- Ex. You calculated the length of a steel pipe to

be 5.2 m. The accepted length is 5.5 m. What is

the percent error?

- Practice 1
- The accepted density for Cu is 8.96 g/mL.

Calculate the percent error for the measurement

8.86 g/mL. - Worksheet

Significant Figures

- Significant figures- include all known digits

plus one estimated digit. - Rules
- Non-zero numbers are always significant
- Ex. 72.3 Ex. 700
- Sandwich zeros are significant.
- 60.5
- 809
- 30.07

Significant Figures

- 3. Final zeros after the decimal are significant.
- a) 6.20
- b) 9.00
- c) 92.0
- d) 0.009200
- 4. Place holding zeros are not significant.
- e) 0.095
- f) 300
- g) 50
- h) 30,000

Significant Figures

- You can convert to scientific notation to remove

place holders. - 30,000 3 x 104
- Example Determine the number of sig figs in the

following masses. - a) 0.000 402 30 g
- b) 405 000 kg
- c) 8.20 x 107
- practice problems p39 31 32

Rounding Off Numbers

- Rounding to 3 sig figs
- 2.5320? if the 4th sig fig is lt5, do not change

the 3rd sig fig. - 2.5360? if the 4th sig fig is gt5, then round the

3rd sig fig up. - Examples
- 55.845 ?(4 sf)
- 32.065 ?(2 sf)
- 87.62 ?(1 sf)
- 36,549,555 ?(2 sf)

Addition/subtraction with sig figs

- Your answer must have the same number of digits

to the right of the decimal as the measurement

with the FEWEST digits to the right of the

decimal. - Ex. Add the following measurements 28.0 cm,

23.538 cm, 25.68 cm.

- practice problems

Multiplication/division w/ sig figs

- Your answer must have the same number of sig figs

as the measurement with the fewest sig figs. - Ex. Calculate the volume of a rectangular object

w/ the following dimensions length 3.65 cm, - width 3.2cm,
- height 2.05 cm.

Multiplication/division w/ sig figs

- practice problems 7-14
- Check old worksheets
- worksheet

Representing Data

- Graph- visual display of data
- Circle graph- usually used to represent

percentages of something.

Representing Data

- Bar graph- often used to show how a quantity

varies with factors such as time, location, or

temperature. - Independent variable- located on the x-axis
- Dependent variable- located on the y-axis

Bar Graph

Representing Data

- Line Graph- most often used in chemistry
- The points on a line graph represent the

intersection of data for 2 variables. - Independent variable- located on the x-axis.
- Dependent variable- located on the y-axis

- Best fit line- line drawn so that as many points

fall above the line as fall below it. - Straight best fit- there is a linear relationship
- The variables are directly related
- Curved best fit- there is a nonlinear

relationship. - The variables are inversely related

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Interpreting Data

- First thing, ID the variables independent

dependent - Notice what measurements were taken
- Decide if the relationship of the variables is

linear/nonlinear.