Chapter 2 Data Analysis p24-51. What is the Mass of the Sun? The mass of the sun= 2 000 000 000 000...

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Chapter 2 Data Analysis p24-51

Transcript of Chapter 2 Data Analysis p24-51. What is the Mass of the Sun? The mass of the sun= 2 000 000 000 000...

Page 1: Chapter 2 Data Analysis p24-51. What is the Mass of the Sun? The mass of the sun= 2 000 000 000 000 000 000 000 000 000 000 000g So how can we write this.

Chapter 2 Data Analysis

p24-51

Page 2: Chapter 2 Data Analysis p24-51. What is the Mass of the Sun? The mass of the sun= 2 000 000 000 000 000 000 000 000 000 000 000g So how can we write this.

What is the Mass of the Sun?

The mass of the sun=2 000 000 000 000 000 000 000 000 000 000 000g

So how can we write this in a simpler way??

Page 3: Chapter 2 Data Analysis p24-51. What is the Mass of the Sun? The mass of the sun= 2 000 000 000 000 000 000 000 000 000 000 000g So how can we write this.

Purpose of Scientific Notation Scientific notation was developed to solve the

problem of writing very large and small numbers.

Numbers written in scientific notation have two parts: a stem, which is a number between 1 & 10, and a power of 10.

93,000,000 = 9.3 x 107

Stem Power of 10

Page 4: Chapter 2 Data Analysis p24-51. What is the Mass of the Sun? The mass of the sun= 2 000 000 000 000 000 000 000 000 000 000 000g So how can we write this.

Purpose of Scientific Notation Let’s take a closer look at the parts of a

number written in scientific notation to see how it works.

The stem is always a number between 1 and 10. In this example, 9.3 is the stem and it is between 1 and 10.

93,000,000 = 9.3 x 107

Stem

Page 5: Chapter 2 Data Analysis p24-51. What is the Mass of the Sun? The mass of the sun= 2 000 000 000 000 000 000 000 000 000 000 000g So how can we write this.

Purpose of Scientific Notation The power of ten has two parts. There is a

base and there is an exponent

The base will always be 10. The exponent in this example is 7.

93,000,000 = 9.3 x 107

Base = 10

Exponent = 7

Page 6: Chapter 2 Data Analysis p24-51. What is the Mass of the Sun? The mass of the sun= 2 000 000 000 000 000 000 000 000 000 000 000g So how can we write this.

Convert Standard Formto Scientific Notation Write 8,760,000,000 in scientific notation.

Step 1: Move the decimal until you have a number between 1 and 10 then drop the extra zeros.

8 7 6 0 0 0 0 0 0 0 ..

8.76 is the Stem

Page 7: Chapter 2 Data Analysis p24-51. What is the Mass of the Sun? The mass of the sun= 2 000 000 000 000 000 000 000 000 000 000 000g So how can we write this.

Convert Standard Formto Scientific Notation Write 8,760,000,000 in scientific notation.

Step 2: The number of places you moved the decimal will be the exponent on the power of 10

8 7 6 0 0 0 0 0 0 0 ..

8.76 is the Stem

9 places

10 9 is the Power of 10

Page 8: Chapter 2 Data Analysis p24-51. What is the Mass of the Sun? The mass of the sun= 2 000 000 000 000 000 000 000 000 000 000 000g So how can we write this.

Convert Standard Formto Scientific Notation Write 8,760,000,000 in scientific notation.

Step 3: Write the number so it is the stem times the power of ten.

8 7 6 0 0 0 0 0 0 0 ..

8.76 is the Stem9 places

10 9 is the Power of 10

8.76 x 10 9 = 8,760,000,000

Page 9: Chapter 2 Data Analysis p24-51. What is the Mass of the Sun? The mass of the sun= 2 000 000 000 000 000 000 000 000 000 000 000g So how can we write this.

Convert Standard Formto Scientific Notation Write the following numbers in scientific notation.

660,000,000 =

90300 =

397 =

6.6 x 108

9.03 x 104

3.97 x 102

Page 10: Chapter 2 Data Analysis p24-51. What is the Mass of the Sun? The mass of the sun= 2 000 000 000 000 000 000 000 000 000 000 000g So how can we write this.

Convert Standard Formto Scientific Notation Write 0.00000000482 in scientific notation.

Step 1: Move the decimal until you have a number between 1 and 10 then drop the extra zeros.

0 0 0 0 0 0 0 0 0 4 8 2. .

4.82 is the Stem

Page 11: Chapter 2 Data Analysis p24-51. What is the Mass of the Sun? The mass of the sun= 2 000 000 000 000 000 000 000 000 000 000 000g So how can we write this.

Convert Standard Formto Scientific Notation Write 0.00000000482 in scientific notation.

0 0 0 0 0 0 0 0 0 4 8 2. .

4.82 is the Stem

Step 2: The number of places you moved the decimal will be the exponent on the power of 10. The exponent will be negative because you started with a number less than 1.

9 places

10 -9 is the Power of 10

Page 12: Chapter 2 Data Analysis p24-51. What is the Mass of the Sun? The mass of the sun= 2 000 000 000 000 000 000 000 000 000 000 000g So how can we write this.

Convert Standard Formto Scientific Notation Write 0.00000000482 in scientific notation.

0 0 0 0 0 0 0 0 0 4 8 2. .

4.82 is the Stem

Step 3: Write the number so it is the stem times the power of ten.

9 places

10 -9 is the Power of 10

4.82 x 10 -9 = 0.00000000482

Page 13: Chapter 2 Data Analysis p24-51. What is the Mass of the Sun? The mass of the sun= 2 000 000 000 000 000 000 000 000 000 000 000g So how can we write this.

Convert Standard Formto Scientific Notation Write the following numbers in scientific notation.

0.00543 =

0.00000074 =

0.03397 =

5.43 x 10 -3

7.4 x 10 -7

3.397 x 10 -2

Page 14: Chapter 2 Data Analysis p24-51. What is the Mass of the Sun? The mass of the sun= 2 000 000 000 000 000 000 000 000 000 000 000g So how can we write this.

Convert Scientific Notationto Standard Form Write 1.98 x 109 in standard form.

The exponent tells us to move the decimal 9 places. A positive exponent means the number is bigger than

the stem. To make 1.98 bigger, we must move the decimal to the right.

1 9 8 x 10 9. 0 0 0 0 0 0 0.

1.98 x 109 = 1,980,000,000

9 places

Page 15: Chapter 2 Data Analysis p24-51. What is the Mass of the Sun? The mass of the sun= 2 000 000 000 000 000 000 000 000 000 000 000g So how can we write this.

Write the following numbers in standard form.

2.9 x 104 =

6.87 x 106 =

1.008 x 109 =

29,000

6,870,0001,008,000,000

Convert Scientific Notationto Standard Form

Page 16: Chapter 2 Data Analysis p24-51. What is the Mass of the Sun? The mass of the sun= 2 000 000 000 000 000 000 000 000 000 000 000g So how can we write this.

Convert Scientific Notationto Standard Form Write 5.37 x 10-9 in standard form.

The exponent tells us to move the decimal 9 places. A negative exponent means the number is smaller

than the stem. To make 5.37 smaller, we must move the decimal to the left.

5 3 7 x 10 -9.0 0 0 0 0 0 0 0 0.

5.37 x 10-9 = 0.00000000537

9 places

Page 17: Chapter 2 Data Analysis p24-51. What is the Mass of the Sun? The mass of the sun= 2 000 000 000 000 000 000 000 000 000 000 000g So how can we write this.

Write the following numbers in standard form.

2.9 x 10-4 =

6.87 x 10-6 =

1.008 x 10-9 =

0.000 29

0.000 006 870.000 000 001 008

Convert Scientific Notationto Standard Form

Page 18: Chapter 2 Data Analysis p24-51. What is the Mass of the Sun? The mass of the sun= 2 000 000 000 000 000 000 000 000 000 000 000g So how can we write this.

What is a standard?

It is an exact quantity that people agree to use for comparison.

Why are measurement standards important?

A meter in the U.S. is the same as a meter in France.

Page 19: Chapter 2 Data Analysis p24-51. What is the Mass of the Sun? The mass of the sun= 2 000 000 000 000 000 000 000 000 000 000 000g So how can we write this.

Units for Measurement Used in Science

Length

Volume

Mass

Temperature

Measured in meters (m)Measured in meters (m)

Measured in liters (L)Measured in liters (L)

Measured in grams (g)Measured in grams (g)

Measured in degrees Celsius (Measured in degrees Celsius (OOC)C)

Metric ruler:

Graduated cylinder:

Balance:

Thermometer:

Page 20: Chapter 2 Data Analysis p24-51. What is the Mass of the Sun? The mass of the sun= 2 000 000 000 000 000 000 000 000 000 000 000g So how can we write this.

International Standard Prefixes (SI)

MUST KNOW:• Kilo = 1,000 or 103

• Centi = .01 or 10-2

• Milli = .001 or 10-3

Page 21: Chapter 2 Data Analysis p24-51. What is the Mass of the Sun? The mass of the sun= 2 000 000 000 000 000 000 000 000 000 000 000g So how can we write this.

Conversions WITHIN the Metric System You can simply move the decimal point…

But you have to know how to move it.

Page 22: Chapter 2 Data Analysis p24-51. What is the Mass of the Sun? The mass of the sun= 2 000 000 000 000 000 000 000 000 000 000 000g So how can we write this.

METRIC UNIT CONVERSIONS

BASE

Move decimal 1 place to the right for each step.

Move decimal 1 place to the left for each step.

Page 23: Chapter 2 Data Analysis p24-51. What is the Mass of the Sun? The mass of the sun= 2 000 000 000 000 000 000 000 000 000 000 000g So how can we write this.

METRIC UNIT CONVERSIONS

Use this to remember the metric prefixes: “King Henry Died Drinking Chocolate Milk” The first letters represent the prefixes (kilo, hecto, deka, deci, centi, milli)

Page 24: Chapter 2 Data Analysis p24-51. What is the Mass of the Sun? The mass of the sun= 2 000 000 000 000 000 000 000 000 000 000 000g So how can we write this.

EXAMPLE

It is common for runners to do a “10K” run. This means they are running 10 kilometers. How many millimeters is that???

A lot!!!!!

Page 25: Chapter 2 Data Analysis p24-51. What is the Mass of the Sun? The mass of the sun= 2 000 000 000 000 000 000 000 000 000 000 000g So how can we write this.

Answer

Look at the staircase graphic… Start on the prefix “kilo” Move down the staircase 6 steps (don’t count

the step you start on) to get to the prefix “milli” This means you move the decimal point 6

places to the RIGHT 10 Kilometers is converted to 10,000,000 mm

Page 26: Chapter 2 Data Analysis p24-51. What is the Mass of the Sun? The mass of the sun= 2 000 000 000 000 000 000 000 000 000 000 000g So how can we write this.

Making Metric Conversions

Make the following metric conversions.– 1,000 grams = kg– 500 mg = g– 2.25 liters = ml– 0.07 g = kg– 1 kilometer = m– 650 cm = m– 0.30 kg = mg

1 0.5 2250 0.00007 1000 6.5 300,000

Table

Home

Page 27: Chapter 2 Data Analysis p24-51. What is the Mass of the Sun? The mass of the sun= 2 000 000 000 000 000 000 000 000 000 000 000g So how can we write this.

Making MetricMeasurements - Length Choose the most appropriate measure.

Length of a football field 1 km, 100 m, 1,000 um, 10 cm, 100 mm

Length of a newborn baby 0.5 m, 0.05 km, 500 um, 5,000mm, 50 cm

Thickness of a sheet of paper 0.1 mm, 0.1 cm, 0.01 m, 1 km, 10 um

Page 28: Chapter 2 Data Analysis p24-51. What is the Mass of the Sun? The mass of the sun= 2 000 000 000 000 000 000 000 000 000 000 000g So how can we write this.

Making MetricMeasurements - Mass The following are approximations to help you get a

feel for metric units of mass. We will deal only with the most common units.

1 kilogram Just over 2 pounds 1 gram Mass of a raisin 1 milligram Mass of a grain of sand

Page 29: Chapter 2 Data Analysis p24-51. What is the Mass of the Sun? The mass of the sun= 2 000 000 000 000 000 000 000 000 000 000 000g So how can we write this.

Making MetricMeasurements - Mass Choose the most appropriate measure.

Mass of a nickel 50 g, 5 mg, 0.5 kg, 5 g, 500 mg

Mass of an aspirin 500 mg, 0.5 mg, 500 g, 50 kg, 50 g

Mass of an average adult 700 kg, 0.7 g, 700 mg, 7,000 g, 70 kg

Mass of a baseball– 400 mg, 0.4 g, 4 kg, 400 g, 40 g

Page 30: Chapter 2 Data Analysis p24-51. What is the Mass of the Sun? The mass of the sun= 2 000 000 000 000 000 000 000 000 000 000 000g So how can we write this.

Making MetricMeasurements - Volume The following are approximations to help you get a

feel for metric units of volume. We will deal only with the most common units.

1 liter Just over 1 quart 1 milliliter About 20 drops

Page 31: Chapter 2 Data Analysis p24-51. What is the Mass of the Sun? The mass of the sun= 2 000 000 000 000 000 000 000 000 000 000 000g So how can we write this.

Making MetricMeasurements - Volume Choose the most appropriate measure.

Volume of a car’s gas tank 50 l, 5 l, 500 ml, 50 ml, 500 l

Volume of a teaspoon 0.5 l, 0.5 ml, 5 l, 5 ml, 500 ml

Volume of a can of soda 500 l, 0.05 l, 500 ml, 0.5 ml, 0.005 ml

Volume of a syringe– 0.02 ml, 200 ml, 0.02 l, 2 l, 2 ml

Page 32: Chapter 2 Data Analysis p24-51. What is the Mass of the Sun? The mass of the sun= 2 000 000 000 000 000 000 000 000 000 000 000g So how can we write this.

centi- meter

milli-liter

kilo-gram

(0.01)

(.001)

(1000)

Putting It All Together

hundredth of a meter

thousandth of a liter

thousand grams

Page 33: Chapter 2 Data Analysis p24-51. What is the Mass of the Sun? The mass of the sun= 2 000 000 000 000 000 000 000 000 000 000 000g So how can we write this.

VII. The Temperature Scales

Kelvin Scale (K) SI Absolute temperature. Same units as Celsius but the freezing point of water is 273K, and the boiling point is 373K.

Celsius Scale ( ˚C) SI common temperature the freezing point of water is 0O C and the boiling point is 100O C.

Fahrenheit Scale (˚F) Used only in the U.S. Water freezing point 32˚F, and boiling point 212˚F.

Page 34: Chapter 2 Data Analysis p24-51. What is the Mass of the Sun? The mass of the sun= 2 000 000 000 000 000 000 000 000 000 000 000g So how can we write this.

Converting from Kelvin to Celsius

TC = TK – 273 ex. ? C = 52K ____˚C = 52K – 273

TK = TC + 273 ex.?K = 70˚C _____K = 70˚C + 273

Page 35: Chapter 2 Data Analysis p24-51. What is the Mass of the Sun? The mass of the sun= 2 000 000 000 000 000 000 000 000 000 000 000g So how can we write this.

Converting from Celsius to Fahrenheit TF = 1.80(TC) + 32

Ex. 41˚C = ? ˚F TF = 1.80 (41˚C) + 32

TF = __________ ˚F

Page 36: Chapter 2 Data Analysis p24-51. What is the Mass of the Sun? The mass of the sun= 2 000 000 000 000 000 000 000 000 000 000 000g So how can we write this.

Making MetricMeasurements Name at least three benefits of the Metric

System.

There is a consistent relationship between units - Prefixes stay the same, It’s easy to convert.

The whole world uses it. The base units are used to “derive” all other

units in the System International (SI)

Home

Page 37: Chapter 2 Data Analysis p24-51. What is the Mass of the Sun? The mass of the sun= 2 000 000 000 000 000 000 000 000 000 000 000g So how can we write this.

Derived units are defined by a combination of base units.

Density = g/cm3

Page 38: Chapter 2 Data Analysis p24-51. What is the Mass of the Sun? The mass of the sun= 2 000 000 000 000 000 000 000 000 000 000 000g So how can we write this.

VII.

Density can be defined as the amount of matter present in a given volume of substance.

Density = mass/ volume

M

D V

Page 39: Chapter 2 Data Analysis p24-51. What is the Mass of the Sun? The mass of the sun= 2 000 000 000 000 000 000 000 000 000 000 000g So how can we write this.

Practice

Mercury has a density of 13.6g/mL. What volume of mercury must be taken to obtain 225g of the metal?

Page 40: Chapter 2 Data Analysis p24-51. What is the Mass of the Sun? The mass of the sun= 2 000 000 000 000 000 000 000 000 000 000 000g So how can we write this.

IV. Accuracy and Precision

Compare and contrast 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.

Page 41: Chapter 2 Data Analysis p24-51. What is the Mass of the Sun? The mass of the sun= 2 000 000 000 000 000 000 000 000 000 000 000g So how can we write this.

Accuracy vs Precision

Is the soda filling machine below accurate and/or precise?

This machine is precise. It delivers the same

amount of soda each time. This machine is not

accurate.– It is not putting 12 oz in

each can.

Page 42: Chapter 2 Data Analysis p24-51. What is the Mass of the Sun? The mass of the sun= 2 000 000 000 000 000 000 000 000 000 000 000g So how can we write this.

Accuracy vs Precision

Is the soda filling machine below accurate and/or precise?

This machine is precise. It delivers the same

amount of soda each time. This machine is accurate.

– It is putting 12 oz in each can.

Page 43: Chapter 2 Data Analysis p24-51. What is the Mass of the Sun? The mass of the sun= 2 000 000 000 000 000 000 000 000 000 000 000g So how can we write this.

Accuracy and Precision cont…

The difference between an accepted value and an experimental value is the error.

The ratio of an error to the correct value, is percent error.

Page 44: Chapter 2 Data Analysis p24-51. What is the Mass of the Sun? The mass of the sun= 2 000 000 000 000 000 000 000 000 000 000 000g So how can we write this.

Formula for Percent Error

= Value accepted – Value experimental x 100%

Value accepted

Page 45: Chapter 2 Data Analysis p24-51. What is the Mass of the Sun? The mass of the sun= 2 000 000 000 000 000 000 000 000 000 000 000g So how can we write this.

Dimensional Analysis

A technique for converting from one unit to another

Page 46: Chapter 2 Data Analysis p24-51. What is the Mass of the Sun? The mass of the sun= 2 000 000 000 000 000 000 000 000 000 000 000g So how can we write this.

Beyond the metric System

If you need to convert to or from units that are NOT metric units, we use a unit conversion technique called “dimensional analysis”

Page 47: Chapter 2 Data Analysis p24-51. What is the Mass of the Sun? The mass of the sun= 2 000 000 000 000 000 000 000 000 000 000 000g So how can we write this.

Conversion Factors

In dimensional analysis, we make conversion factors into fractions that we will multiply by.

For example, one conversion factor is: 1 inch=2.54 cm We can make (2) fractions out of this… 1 inch OR 2.54 cm

2.54 cm 1 inch

Page 48: Chapter 2 Data Analysis p24-51. What is the Mass of the Sun? The mass of the sun= 2 000 000 000 000 000 000 000 000 000 000 000g So how can we write this.

Which number goes on top and bottom in the conversion factor? Usually… The unit you WANT goes on TOP The unit you want to CANCEL goes on

BOTTOM

Page 49: Chapter 2 Data Analysis p24-51. What is the Mass of the Sun? The mass of the sun= 2 000 000 000 000 000 000 000 000 000 000 000g So how can we write this.

Dimensional Analysis EXAMPLE

A PENCIL IS 17.8 CM LONG, WHAT IS ITS LENGTH IN INCHES? Start with the “given” 17.8 cm

Page 50: Chapter 2 Data Analysis p24-51. What is the Mass of the Sun? The mass of the sun= 2 000 000 000 000 000 000 000 000 000 000 000g So how can we write this.

Dimensional Analysis

A PENCIL IS 17.8 CM LONG, WHAT IS ITS LENGTH IN INCHES? Multiply by the “conversion factor” 17.8 cm x 1 inch =

2.54 cm

Page 51: Chapter 2 Data Analysis p24-51. What is the Mass of the Sun? The mass of the sun= 2 000 000 000 000 000 000 000 000 000 000 000g So how can we write this.

Dimensional Analysis

A PENCIL IS 17.8 CM LONG, WHAT IS ITS LENGTH IN INCHES? Cross cancel “like” units

17.8 cm x 1 inch

2.54 cm

Page 52: Chapter 2 Data Analysis p24-51. What is the Mass of the Sun? The mass of the sun= 2 000 000 000 000 000 000 000 000 000 000 000g So how can we write this.

Dimensional Analysis

A PENCIL IS 17.8 CM LONG, WHAT IS ITS LENGTH IN INCHES? Do the math using the correct number of

significant figures (based on given information)17.8 cm x 1 inch = 7.01 inches

2.54 cm

Page 53: Chapter 2 Data Analysis p24-51. What is the Mass of the Sun? The mass of the sun= 2 000 000 000 000 000 000 000 000 000 000 000g So how can we write this.

Dimensional Analysis Example

A pencil is 8.1 inches, how many cm is it? 8.1 inches x 2.54 cm = 21 cm

1 inch

The unit we WANT is cm so we put 2.54 cm on TOP of the conversion factor

Page 54: Chapter 2 Data Analysis p24-51. What is the Mass of the Sun? The mass of the sun= 2 000 000 000 000 000 000 000 000 000 000 000g So how can we write this.

Multi-Step Example

Sometimes, we must “string” several conversion factors together to get from one unit to another. Ex.- Mr. Gray’s class is 55 minutes long. How

many days long is this??!!

Page 55: Chapter 2 Data Analysis p24-51. What is the Mass of the Sun? The mass of the sun= 2 000 000 000 000 000 000 000 000 000 000 000g So how can we write this.

Multi-Step Example

Need to go from min hrs days 55 min x 1 hr x 1 day = 0.038 days

60 min 24 hrs

Note how “like” units can be cross-canceled (canceled out)

Page 56: Chapter 2 Data Analysis p24-51. What is the Mass of the Sun? The mass of the sun= 2 000 000 000 000 000 000 000 000 000 000 000g So how can we write this.

Practice

Perform each of the following conversions, being sure to set up clearly the appropriate conversion factor in each case.

1. 55min to hours2. 6.25km to miles3. Apples cost $0.79 per pound. How

much does 5.3 lb of apples cost?

Page 57: Chapter 2 Data Analysis p24-51. What is the Mass of the Sun? The mass of the sun= 2 000 000 000 000 000 000 000 000 000 000 000g So how can we write this.

Significant Figures

Significant figures include the number of all known digits reported in measurement plus one estimated digit.

1. Non-zero numbers are always significant

2. Zeros between non-zero #s are always significant

3. All final zeros to the right of the decimal place are significant

Page 58: Chapter 2 Data Analysis p24-51. What is the Mass of the Sun? The mass of the sun= 2 000 000 000 000 000 000 000 000 000 000 000g So how can we write this.

Significant rules cont.

4. Zeros that act as placeholders to the left of the decimal are not significant. Positive exponents in scientific notation are not significant.

5. Zeros that are to the right of the decimal are always significant. Negative exponents!

6. Counting numbers and defined constants have an infinite number of significant figures.