CHAPTER 2 OUTLINE begin on page 28 - Mrs. Perry's ...



CHAPTER 2 OUTLINE – ANALYZING DATA Name__________________________________

Section 2.1 Units and Measurements

Objectives:

o Define SI units

o Prefix usage

o Compare derived units

Answer the following; begin on page 32

1. What does “SI” stand for? How does it compare to the “metric” system.

2. Define base unit.

List them here, and the quantity they measure:

|Quantity |Base unit |

| | |

| | |

| | |

| | |

| | |

| | |

| | |

3. In the table, list the common SI prefixes, their symbols, their numerical value, and the power of ten equivalent:

|Prefix |Symbol |Numerical value |Power of ten equivalent |

| | | | |

| | | | |

| | | | |

| | | | |

| | | | |

| | | | |

| | | | |

| | | | |

| | | | |

| | | | |

4. What is the physical standard used to define the second.

5. Define meter.

6. Where does a vacuum exist?

7. A meter is close in length to what English system unit?

8. What is the SI base unit for mass? What defines it?

9. How many pounds are in a kilogram? Why don’t scientists use a kilogram often?

10. Define temperature and state what instrument measures it.

11. List the three temperature scales commonly used.

12. What is the equation that would calculate Fahrenheit given a Celsius value?

13. What is the Kelvin-Celsius conversion equation?

14. In Kelvin, what temperature does water freeze? What Kelvin temperature does water boil at?

15. Use the equations in number 12 and 13 and convert these values to Celsius and Fahrenheit

16. Define derived unit.

17. State three quantities that are measured using derived units.

18. Define volume. How can it be measured?

19. Define liter.

20. One milliliter is the same as what cubic unit? One liter is the same as what cubic unit?

21. Define density and units used to measure it.

22. An element has a density of 2.7 g/cm3. Use table R-7 (beginning on p 971) in the back of the book to try to identify this element.

23. An element has a mass of 48.25 grams and a volume of 2.5 mL. What is its density? What element might it be (see table R-7).

Temperature scales and converting Name________________________

(F = ((C x 1.8) + 32 K = (C + 273

(C = ((F – 32) ÷ 1.8 (C = K-273

Convert the following to Fahrenheit

1) 10o C ________

2) -30o C ________

3) 40o C ________

4) 237 K________

5) -100o C ________

6) 150 K_________

Convert the following to Celsius

7) 32o F ________

8) -40o F ________

9) 70o F ________

10) 350 o F ________

11) -90o F ________ Convert the following to Kelvin

12) 212o F ________ 18) 0o C ________

13) 100K ________ 19) -50o C ________

14) 20 K ________ 20 90o C ________

15) 273 K ________ 21) -20o C ________

16) 350 K ________ 22) 65 o F ________

17) 500 K ________ 23) -260 o F ________

Density Intro

Mass is measured in grams (g)

Volume is measure in milliliters (mL) or cm3

Density equation: [pic]

The density of water is 1.00 g/mL . Anything with a density greater than 1.00 g/mL will sink; if it’s lower, it will float.

Examples:

1. What is the density of 2.78 grams of a liquid that occupies 1.50 mL? Does it sink or float on water?

2. What is the density of 3.75 cm3 of a substance that has a mass of 3.13 g? Does it sink or float on water?

3. What is the mass of 125 mL of mercury that has a density of 13.6 g/cm3?

4. What volume would 45.7 g of a substance occupy that has a density of 0.897 g/mL?

Section 2.2 Scientific notation and dimensional analysis

Objectives:

o Express numbers in scientific notation

o Convert between units using dimensional analysis

1. Define Scientific Notation

2. Other information:

• This is a way of handling really big or really small numbers in calculators.

• Examples:

▪ 564 200 000 000 000 is equal to 5.642 x 1014

▪ 0.000 000 000 000 000 000 000 012 is equal to 1.2 x 10 -23

• Note that the 1st number must be between 1 and 10, but not include 10

• The exponent tells how many places to move the decimal

• A positive exponent is a big number; greater than ten

• A negative exponent is a small number; less than 1, but greater than zero.

• note: we often won’t use commas, just spacing

Convert each to scientific notation: Take each out of scientific notation:

1. 2400 1. 1.2 x 105

2. .000046 2. 6 x 10-8

3. 135990000 3. 5.89 x 10-1

4. 0.5 4. 3.06 x 100

5. 67 5. 2.689 x 102

6. 54000000000 6. 1.597 x 10-3

7. .00000000000086 7. 2.034 x 10 15

3. How do you add or subtract numbers in scientific notation?

Two ways:

a) Must be same exponent or b) take out of scientific notation

Examples:

1. (1.2 x 104 ) + (3.5 x 10 4) = 2. (1.5 x 104 )+ (2.6 x 103)

4. How do you multiply or divide in scientific notation?

a) Multiply or divide the coefficients then work with exponents

(when multiplying, add exponents; when dividing, subtract exponents)

Examples:

1. (1.2 x 104 ) x (3.5 x 10 -9) = 2. (1.5 x 104 ) ÷ (2.6 x 10-5)

Define Dimensional Analysis

Define Conversion Factor

Converting using Dimensional Analysis

1. Always write down the given value as a fraction ÷ one

2. Set up conversion factor(s)

a. Work first with units so that everything cancels to give just the unit you want

b. Make sure every numerator = every denominator

3. Do the math!!!

a. Multiply just like any fraction; multiply across all the numerators, and divide by any denominator(s)

4. Use as many significant digits in your answer as there are in the original problem.

Convert each:

1. 15 lbs to oz

2. 200. pts to gal

3. 7 in to ft

4. 7 in2 to ft2

5. 7 in3 to ft3

6. 25 miles/hour to ft/min

7. 34 kg to g

8. 25 g to mg

9. 250 mg to μg

10. 6.7 x 106 kL to ML

11. 1.21 GWatts to TWatts

12. 8.97 x 105 ng to pg

Section 2.3 Uncertainty in Data

Objectives:

▪ Define and compare accuracy and precision

▪ Describe accuracy of an experiment using error and percent error

▪ Apply rule of significant figures to express uncertainty in measurements and calculations

1. Define accuracy

2. Define precision

3. Define error and state its formula

4. Define percent error and state its formula

5. Do number 33 on page 49

6. Do numbers 93 & 94 on page 63

7. Define significant figures.

SIGNIFICANT DIGITS OR SIGNIFICANT FIGURES

• Defined as all the actually measured digits

• Includes all digits known with certainty, plus one uncertain digit (the estimated one) – All measurements include one uncertain digit! (the last digit!)

• Ex: 134.76 lbs has ________ significant figures. The last digit ____ is estimated and is still significant

• Rules to recognize sig figs

1. all nonzero digits are significant

• 456 meters has _________sig figs; the number ________ is estimated

2. Zeros in between other sig figs are significant [sandwich rule!]

• 30.52 grams has________ sig figs; the number _________ is estimated

3. Final zeros after the decimal and at the end of a measurement are significant

• 4.50 mL has ________ sig figs; the number _________ is estimated

• 603.030 mg has _________ sig figs; the number _______ is estimated

4. Leading zeros and placeholder zeros are not significant [placeholder zeros tell you how big or small a value is; they are the “10n” part of scientific notation.]

• 45,500 has ______ sig figs

• 0.0025 has ______sig figs

• 1.25 x 104 has ______ sig figs

• 1.10 x 10-6 has _______sig figs

• How to make a nonsignificant zero significant: For example, if you have the measurement 250 pounds and want to show that the last zero is significant.

a) Put in a deliberate decimal:

• 250 pounds has ____ sig figs

• 250. pounds has ____ sig figs

b) Put value in scientific notation (often used in your book)

• 2.50 x 102 pounds has _______ sig figs

c) Put a bar over the zero (rarely used anymore)

• 250 pounds has _____ sig figs

• Note: counting numbers have not been measured and have an infinite number of sig figs; that is, sig fig rules don’t apply!

• Ex: 45 cars or 50 people are counting numbers and have infinite sig figs

How many sig figs in each?

|456 grams |2.0 meters |

|708 seconds |4000 pounds |

|0.002 liters |0.10 % |

|0.005006 grams |60 pencils |

|93 000 000 miles |2500 amperes |

|25ŌO amperes |2.500 x 103 amperes |

|2.5000 x 103 amperes |2500.0 amperes |

|0.024 milliliters |235 cats |

Sig fig question: Show the measurement 575400 grams to have:

|1 sig fig |2 sig figs |

|3 sig figs |4 sig figs |

|5 sig figs |6 sig figs |

|7 sig figs |8 sig figs |

Math operations w/ sig figs (that is, How to round calculated answers using significant digits)

• When multiplying and dividing, your answer can only have as many sig figs as the number in the problem with the least number of sig figs. COUNT THOSE SIG FIGS!!!

2.2 in x 4.53 in = ______________ from your calculator but __________ in proper sig figs

45.78 grams ÷ 2.58 mL = ______________ from your calculator, but __________ in sig figs

2.5 x 102 ft x 7.4 x 104 ft =____________ from your calculator but ______________ in sig figs

• When adding and subtracting, your answer can only be as accurate (to a certain decimal place) as the number in the problem that is the least accurate. LOOK AT DECIMAL PLACE OF LAST SIG FIG!!!

34.6 g + 0.57 g = ________________ from your calculator but _____________ in sig figs

0.05830 g + 0.00009832 g = ______________ from calculator but _____________ in sig figs

4.16 mL + 0.840 mL = _________ from a calculator but ____________ in sig figs

12500 lb – 760 lb = ____________ from calculator but ____________ in sig figs

145 lb + 0.023 lb = ____________ from a calculator bu ___________ in sig figs

Examples:

|4.5m x 0.39 m |0.06mile x 0.08mile |

|450ft x 34ft x 87ft |3.45 L + 4.7258 L |

|0.002 m – 0.000627 m |36 g ÷ 5.0mL |

|22 000m x 45 900m |895m3 x 2.1m |

|5ft x 7ft |5.0 ft x 7.0 ft |

|5.00 ft x 7.00 ft |0.00045 in x 0.000085 in |

|34.5in + 5.678 in |240g + 8900 g |

|95,000 m + 6,700 m |1.25 g – 0.0000035 g |

Section 2.4 Representing data

Objectives:

• Create and interpret graphs

Define each word:

1. Graph

2. Circle graph

3. Bar graph

4. Line graph

5. Independent variable

6. Dependent variable

7. Slope equation

8. Interpolation

9. Extrapolation

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