Scientific Notation & Units Problem Solving Scientific Notation & Units Section 5.1 & 5.3A Period #6 Group #3

This cartoon explains the importance of numbers & units today. Background Measurements such as “fathom,” “rod,” and “cubit” were inaccurate units of measurements used in the past. http://lamar.colostate.edu/~hillger/toles-orbiter.gif Side 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. This cartoon explains the importance of numbers & units today.

Peanuts Background Cartoon http://hawaii.hawaii.edu/math/Courses/Math100/Chapter1/Text/G1/Peanuts.jpg

Scientific Notation Scientific 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

Conversion of Large 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)

Conversion of Small Numbers  Scientific Notation Number in standard notation Move the decimal to the right  until it goes past the first non-zero digit Cross out the zeros in front Rewrite the number and multiply it by 10^(# of times you moved the decimal the right)

Example Q: Explain the error in the following conversion. Write the correct scientific notation. 0.00217  21.7 x 10-4 A: The error is that scientific notation expresses a product of a power between 1 & 10 and the appropriate power of 10. In this case, 21.7 is not a number between 1 and 10. The correct scientific notation is 2.17 x 10-3.

Units 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 based on Metric System 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.

Commonly Used Prefixes in the Metric System Units Common Fundamental SI Units Quality Name of Unit Abbreviation Mass kilogram kg Length meter m Time second s Temperature kelvin K Commonly Used Prefixes in the Metric System 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 Because fundamental units are not always a convenient size, the SI system uses prefixes to change the size of the unit to accommodate them.

Example Q: Why are prefixes such as mega, kilo-, deci-, centi-, milli-, etc. needed? A: Because fundamental units are not always a convenient size, the SI system uses prefixes to change the size of the unit to accommodate them.

Measurements of Length, Mass, & Volume 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 & Volume Commonly Used Metric Units for Length Unit Symbol Equivalence Kilometer km 1000m Meter m 1 m Decimeter dm 0.1m Centimeter cm 0.01 m Millimeter mm 0.001m Commonly Used Metric Units for Volume Unit Symbol Equivalence Liter L 1L = 1000 mL= 1 dc3 Milliliter mL 1 mL = 0.001L = 1 cm3 Commonly Used Metric Units for Mass Unit Symbol Equivalence Kilogram kg 1 kg = 1000 g Gram g 1 g Milligram mg 1 mg = 0.001 g

Measurements of Length, Mass, & Volume 1kg = 1000g 1mg = 0.001g 1g = 1000mg http://i.ehow.com/images/GlobalPhoto/Articles/5305130/322781_Full.jpg http://www.teachthis.com.au/images/prod_photos/1223620271Measurement_Charts.jpg

Example Q: How does a kilometer compare to a meter? How does a milliliter compare to a liter? A: A kilometer is 1000 meters while a milliliter is 0.001 liter.

Problem Solving Problem Solving Ask yourself these questions… Attack problem systematically: Ask yourself these questions… Where do we want to go? What do we know? How do we get there? Does it make sense? Problem Solving http://api.ning.com/files/9yAp4sIjSZerFihUCkXB1w*gKhYlUkNCNQUy12J0cgkdYSIRCKqzy9a2*RUeVQueCyE5-l96BTpGvt*LTesthWekoWJClMJm/questions.jpeg

Example Q: What are some of the questions that could be used to arrive at a solution? A: Where do we want to go? What do we know? How do we get there? Does it make sense?

Unit Conversions Convert Units: 2. Choose the conversion factor 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 to 1. Find an equivalence statement that relates the 2 units Convert Units: 2. Choose the conversion factor 3. Multiply the quantity by the conversion factor 4. Check to make sure you have correct # of significant factors

Unit Conversions Picture includes multiple systems of measurements in equivalent statements. A humorous cartoon which depicts the unit conversion when people travel to other countries. http://www.ssportsman.com/wordpress/wp-content/uploads/2009/02/metric-system-cartoon.gif http://water.usgs.gov/nwsum/WSP2425/images/conversion.gif

Example Q: Define dimensional analysis in your own words. A: Dimensional analysis is to change one system of units to another by using conversion factors.

Quiz 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 Answers Scientific Notation Units The value of A is 26,700 and the value of B is 28,700. Choice B is the greater value. Units Units 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 Units To 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.

Sources 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