Transcript 1 inch - Fort Bend ISD

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.
93,000,000 = 9.3 x 107
Stem
 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.
Purpose of
Scientific Notation
 The power of ten has two parts. There is a
base and there is an exponent
Exponent = 7
93,000,000 = 9.3 x 107
Base = 10
 The base will always be 10.
 The exponent in this example is 7.
Convert Standard Form
to 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 Form
to 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 .
9 places
8.76 is the Stem
10 9 is the Power of 10
Convert Standard Form
to 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 .
9 places
8.76 is the Stem
10 9 is the Power of 10
8.76 x 10 9 = 8,760,000,000
Convert Standard Form
to Scientific Notation
 Write the following numbers in scientific
notation.
660,000,000 = 6.6 x 108
90300
= 9.03 x 104
397
= 3.97 x 102
Convert Standard Form
to 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 Form
to Scientific Notation
 Write 0.00000000482 in scientific notation.
 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.
0.0 0 0 0 0 0 0 0 4 . 8 2
9 places
4.82 is the Stem
10 -9 is the Power of 10
Convert Standard Form
to Scientific Notation
 Write 0.00000000482 in scientific notation.
 Step 3: Write the number so it is the stem times the
power of ten.
0.0 0 0 0 0 0 0 0 4 . 8 2
9 places
4.82 is the Stem
10 -9 is the Power of 10
4.82 x 10 -9 = 0.00000000482
Convert Standard Form
to Scientific Notation
 Write the following numbers in scientific
notation.
0.00543
= 5.43 x 10 -3
0.00000074 = 7.4 x 10 -7
0.03397
= 3.397 x 10 -2
Convert Scientific Notation
to 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.
0 09 0 0 0 .
1.9 8 0x 010
9 places
1.98 x 109 = 1,980,000,000
Convert Scientific Notation
to Standard Form
 Write the following numbers in standard form.
2.9 x 104 = 29,000
6.87 x 106 = 6,870,000
1.008 x 109 = 1,008,000,000
Convert Scientific Notation
to 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.
0.0 0 0 0 0 0 0 0 5. 3 7 x 10 -9
9 places
5.37 x 10-9 = 0.00000000537
Convert Scientific Notation
to Standard Form
 Write the following numbers in standard form.
2.9 x 10-4 = 0.000 29
6.87 x 10-6 = 0.000 006 87
1.008 x 10-9 = 0.000 000 001 008
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
Metric ruler:
Measured in meters (m)
Volume
Graduated cylinder:
Measured in liters (L)
Mass
Balance:
Measured in grams (g)
Temperature
Thermometer:
Measured in degrees Celsius (OC)
International Standard Prefixes (SI)
Prefix
Symbol
Factor Number
Factor Word
Kilo
Hecto
Deka
Deci
Centi
Milli
k
h
da
d
c
m
1,000
100
10
0.1
0.01
0.001
Thousand
Hundred
Ten
Tenth
Hundredth
Thousandth
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
Move decimal 1 place to the right for each step.
BASE
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
Home
 Make the following metric conversions.
–
–
–
–
–
–
–
1,000 grams = 1
kg
500 mg =
g
0.5
2.25 liters
= 2250 ml
0.07 g
= 0.00007 kg
1 kilometer
= 1000 m
650 cm =
m
6.5
0.30 kg =
300,000 mg
Table
Making Metric
Measurements - 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 Metric
Measurements - 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 Metric
Measurements - 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 Metric
Measurements - 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 Metric
Measurements - 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
Putting It All Together
centi(0.01)
meter
hundredth of a meter
milli(.001)
liter
thousandth of a liter
kilo(1000)
gram
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
= 70˚C
 _____K = 70˚C + 273
 ex.?K
Converting from Celsius to
Fahrenheit
 TF = 1.80(TC) + 32
Ex. 41˚C = ? ˚F
TF = 1.80 (41˚C) + 32
TF = __________ ˚F
Making Metric
Measurements
Home
 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)
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
2.54 cm
= 7.01 inches
Dimensional Analysis Example
 A pencil is 8.1 inches, how many cm is it?

8.1 inches
x
2.54 cm
1 inch
=
21 cm
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
60 min
1 day
24 hrs
Note how “like” units can be
cross-canceled (canceled out)
= 0.038 days
Practice
 Perform each of the following
conversions, being sure to set up
clearly the appropriate conversion
factor in each case.
1. 55min to hours
2. 6.25km to miles
3. 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.