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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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...
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 in a simpler way??
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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.
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:
International Standard Prefixes (SI)
MUST KNOW:• Kilo = 1,000 or 103
• Centi = .01 or 10-2
• Milli = .001 or 10-3
Conversions WITHIN the Metric System You can simply move the decimal point…
But you have to know how to move it.
METRIC UNIT CONVERSIONS
BASE
Move decimal 1 place to the right for each step.
Move decimal 1 place to the left for each step.
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)
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!!!!!
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
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
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
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
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
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
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
centi- meter
milli-liter
kilo-gram
(0.01)
(.001)
(1000)
Putting It All Together
hundredth of a meter
thousandth of a liter
thousand grams
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.
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
Converting from Celsius to Fahrenheit TF = 1.80(TC) + 32
Ex. 41˚C = ? ˚F TF = 1.80 (41˚C) + 32
TF = __________ ˚F
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
Derived units are defined by a combination of base units.
Density = g/cm3
VII.
Density can be defined as the amount of matter present in a given volume of substance.
Density = mass/ volume
M
D V
Practice
Mercury has a density of 13.6g/mL. What volume of mercury must be taken to obtain 225g of the metal?
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.
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.
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.
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.
Formula for Percent Error
= Value accepted – Value experimental x 100%
Value accepted
Dimensional Analysis
A technique for converting from one unit to another
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”
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
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
Dimensional Analysis EXAMPLE
A PENCIL IS 17.8 CM LONG, WHAT IS ITS LENGTH IN INCHES? Start with the “given” 17.8 cm
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
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
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
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
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??!!
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)
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?
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
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.