problem solving scientific notation & units period #6 group #3 section 5.1 & 5.3a
TRANSCRIPT
Problem SolvingProblem SolvingScientific Notation & Units
Period #6Period #6Group #3Group #3
Section 5.1 & 5.3ASection 5.1 & 5.3A
BackgroundBackground
Side NoteSide Note: NASA sent a $125 million dollars spacecraft off–course on its way to Mars due to use of English units instead of metric. This is a cartoon that is based off NASA’s blunder and which demonstrates
NASA’s confusing directions.
Side NoteSide Note: NASA sent a $125 million dollars spacecraft off–course on its way to Mars due to use of English units instead of metric. This is a cartoon that is based off NASA’s blunder and which demonstrates
NASA’s confusing directions.
http://lamar.colostate.edu/~hillger/toles-orbiter.gif
Measurements such as “fathom,” “rod,”
and “cubit” were inaccurateinaccurate units of
measurements used in the past.
Measurements such as “fathom,” “rod,”
and “cubit” were inaccurateinaccurate units of
measurements used in the past.
This cartoon explains the importanceimportance of numbers & units today. This cartoon explains the importanceimportance of numbers & units today.
Background CartoonBackground Cartoon
http://hawaii.hawaii.edu/math/Courses/Math100/Chapter1/Text/G1/Peanuts.jpg
Scientific NotationScientific NotationScientific Notation: expresses a number as a product of a number between 1 & 10 and the appropriate power of 10 Purpose: to express a large or small quantity without using many unnecessary zeros
http://www.rjdposters.com/Content/Store/404239143-Alg932.jpg
Scientific NotationScientific Notation
Conversion of LargeLarge Numbers Scientific Notation
1. Number in standard notation
2. Add a decimal after last digit
3. Move decimal to the left (only 1 digit left in front)
4. Cross out zeros at the end
5. Rewrite # as the decimal multiply it by
10^(# of times you moved the decimal to the left)
Scientific NotationScientific Notation
Conversion of SmallSmall Numbers Scientific Notation
1. Number in standard notation
2. Move the decimal to the right until it goes past the first non-zero digit
3. Cross out the zeros in front
4. Rewrite the number and multiply it by
10^(# of times you moved the decimal the right)
ExampleExampleQ: Explain the error in the following Q: Explain the error in the following
conversion. Write the correct scientific conversion. Write the correct scientific notation.notation.
0.00217 0.00217 21.7 x 10 21.7 x 10-4-4
A: The error is that scientific notation expresses a A: The error is that scientific notation expresses a product of a power between 1 & 10 and the product of a power between 1 & 10 and the appropriate power of 10. In this case, 21.7 is not a appropriate power of 10. In this case, 21.7 is not a number between 1 and 10. The correct scientific number between 1 and 10. The correct scientific notation is 2.17 x 10notation is 2.17 x 10-3-3..
UnitsUnits Unit: the part of the measurement that
tells us the scale/standard being used
(quantitative part of measurement)
Used by Examples
Metric System
**SI unit SI unit based based on Metric on Metric SystemSystem
Most of the world
Meters, grams,
kilometers, centimeters,
liters
English system
United States Pounds, ounces, cups, feet, inches,
miles
http://members.pioneer.net/~mchumor/00images/6947_metric_cartoon.gif
This cartoon expresses the importance of units and describes the difficulty with two measurement systems.
UnitsUnits
Prefix Symbol Meaning Power of 10
Mega M 1,000,000 106
Kilo k 1000 103
Deci d 0.1 10-1
Centi c 0.01 10-2
Milli m 0.001 10-3
Micro µ 0.000001 10-6
Nano n 0.000000001 10-9
CommonCommon Fundamental SI Units
CommonlyCommonly Used Prefixes in the Metric System
Because fundamental units are not always a convenient size,
the SI system uses prefixesprefixes to change change the size of the unit the size of the unit to accommodate
them.
Because fundamental units are not always a convenient size,
the SI system uses prefixesprefixes to change change the size of the unit the size of the unit to accommodate
them.
ExampleExampleQ: Why are prefixes such as mega,Q: Why are prefixes such as mega,
kilo-, deci-, centi-, milli-, etc. needed?kilo-, deci-, centi-, milli-, etc. needed?
A: A: Because fundamental units are not Because fundamental units are not
always a convenient size, the SI system always a convenient size, the SI system
uses prefixes to uses prefixes to change the size of the unit change the size of the unit
to accommodate them.to accommodate them.
Measurements of Length, Mass, & Measurements of Length, Mass, & VolumeVolume
Length – the distance of an object measured end to end
• SI unit of length is meter Volume – amount of 3D space occupied by a substance (length x width x height)
• SI unit is the cubic meter (m3)
• Liquids are measured in liters (dm3) & millimeters (cm3) Mass – a quantity of matter present in an object
• Metric unit is gram
• SI unit is kilogram
Measurements of Length, Mass & Measurements of Length, Mass & VolumeVolume
UnitUnit SymbolSymbol EquivalenceEquivalence
Kilometer km 1000m
Meter m 1 m
Decimeter dm 0.1m
Centimeter cm 0.01 m
Millimeter mm 0.001m
UnitUnit SymbolSymbol EquivalenceEquivalence
Liter L 1L = 1000 mL= 1 dc3
Milliliter mL 1 mL = 0.001L = 1 cm3
UnitUnit SymbolSymbol EquivalenceEquivalence
Kilogram kg 1 kg = 1000 g
Gram g 1 g
Milligram mg 1 mg = 0.001 g
Commonly Used Metric Units for LengthMetric Units for Length
Commonly Used Metric Units for VolumeMetric Units for Volume
Commonly Used Metric Units for MassMetric Units for Mass
Measurements of Length, Mass, & Measurements of Length, Mass, & VolumeVolume
http://www.teachthis.com.au/images/prod_photos/1223620271Measurement_Charts.jpghttp://i.ehow.com/images/GlobalPhoto/Articles/5305130/322781_Full.jpg
MassMass
1kg = 1000g1kg = 1000g1mg = 0.001g1mg = 0.001g1g = 1000mg1g = 1000mg
ExampleExample Q: How does a kilometer compare Q: How does a kilometer compare
to a meter? How does a milliliter to a meter? How does a milliliter compare to a liter?compare to a liter?
A: A kilometer is 1000 meters while a A: A kilometer is 1000 meters while a milliliter is 0.001 liter.milliliter is 0.001 liter.
Problem SolvingProblem Solving
Problem SolvingProblem SolvingProblem SolvingProblem Solving
Attack problem systematicallysystematically:
Ask yourself these questions… Where do we want to go? What do we know? How do we get there? Does it make sense?
http://api.ning.com/files/9yAp4sIjSZerFihUCkXB1w*gKhYlUkNCNQUy12J0cgkdYSI
RCKqzy9a2*RUeVQueCyE5-l96BTpGvt*LTesthWekoWJClMJm/questions.jpeg
ExampleExample Q: What are some of the questions that Q: What are some of the questions that
could be used to arrive at a solution?could be used to arrive at a solution?
A: Where do we want to go?A: Where do we want to go?
What do we know?What do we know?
How do we get there?How do we get there?
Does it make sense?Does it make sense?
Unit ConversionsUnit Conversions Dimensional Analysis – to convert one system of units to another by using
conversion factors Equivalence Statement - shows relationship between units of different systems
Ex: 2.54 cm = 1 in. Conversion Factor - are ratios of the 2 parts of the equivalence statement.
Ex: 2.54 cm or 1 in.
1 in. 2.54 cm
Steps toSteps to 1. Find an equivalence statement that relates the 2 units1. Find an equivalence statement that relates the 2 units
Convert UnitsConvert Units:: 2. Choose the conversion factor 2. Choose the conversion factor
3. Multiply the quantity by the conversion factor3. Multiply the quantity by the conversion factor
4. Check to make sure you have correct # of significant factors4. Check to make sure you have correct # of significant factors
Unit ConversionsUnit ConversionsPicture includes multiple systems
of measurements in equivalent statements.
Picture includes multiple systems
of measurements in equivalent statements.
http://water.usgs.gov/nwsum/WSP2425/images/conversion.gifhttp://www.ssportsman.com/wordpress/wp-content/uploads/
2009/02/metric-system-cartoon.gif
A humorous cartoon which depicts the unit conversion when people travel to other countries.
A humorous cartoon which depicts the unit conversion when people travel to other countries.
ExampleExample Q: Define dimensional analysis in Q: Define dimensional analysis in
your own words.your own words.
A: Dimensional analysis is to change one A: Dimensional analysis is to change one system of units to another by using system of units to another by using conversion factors. conversion factors.
Quiz on 5.1 & 5.3AQuiz on 5.1 & 5.3A• Scientific Notation
Solve each of the following. Which of the two measurements is greater?
a.) 2.67 x 104 b.) 287. 2 x 102
• Units
Are units the qualitative or quantitative part of a measurement? Explain?
• Measurements of Length, Mass, & Volume
What is mass and its SI unit?
• Problem Solving
Give an everyday example of how dimensional analysis has helped you in life.
• Converting Units
What must we use to convert units?
Quiz AnswersQuiz Answers• Scientific NotationThe value of A is 26,700 and the value of B is 28,700. Choice B is the
greater value.
• UnitsUnits are a quantitative part of a measurement because it describes the
amount.
• Measurements of Length, Mass, & Volume
Mass is the quantity of matter present in an object. Its SI unit is kilogram.
• Problem Solving
(Answers will vary. Check if answers relate to converting units to achieve something.)
• Converting UnitsTo be able to convert units, you must use an equivalence statement that
relates the 2 different units in the equation. Then, you must turn the equivalence statement into a conversion factor to get the desired unit.
SourcesSources• Scientific Notation Explanation
http://www.docstoc.com/docs/2281115/What-is-Scientific-Notation
http://www.purplemath.com/modules/exponent3.htm
• Scientific Notation Exercises
http://www.purplemath.com/modules/exponent3.htm (highly recommended)
http://janus.astro.umd.edu/cgi-bin/astro/scinote.pl
• Converting Units
http://www.docstoc.com/docs/2366000/Review-of-Units-and-Intro-to-Unit-Conversion