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