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Mastering Scientific Notation: Big & Small Numbers in Science

Learn how to represent large and small numbers in scientific notation, essential for scientific measurements. Understand units, prefixes, and problem-solving strategies with examples and questions answered.

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Mastering Scientific Notation: Big & Small Numbers in Science

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  1. Section 5.1 and 5.3 (a)Group 3 Period 5

  2. Scientific Notation Numbers used in science is really big or really small.  The numbers can be the measurements of the thickness of a dime (1.35 mm) or the distance between France and America (7,700 km). Scientific notation is simply a method for making very big or very small numbers easier to write. **Note: Scientific Notation shows a number as a product of a number between 1 and 10 and a power of 10.

  3. ~|Representing Large Numbers|~ The distance between America and France is 7,700 km. • Write the number • Put a decimal right after the last digit. Now take this decimal and move it to the left until there’s a number b/w 1 and 10 in front of it. • To find the number on top of the exponent count how many spaces the decimal point moved.

  4. Example of representing large numbers EX: 1)7,700   2) 7,700. put decimal 7.700 3) Count the number of spaces the decimal moved to get the exponent 7.7 x 10³

  5. -5

  6. ~|Representing Small Numbers|~ The thickness of a dime is 1.35 mm or .00135 meters. • Write the number • Move the decimal to the right until it passes the first non zero number. ** Make sure the number is between 1 and 10 • To find the number on top of the exponent count how many spaces the decimal point moved.

  7. Example of representing small numbers EXAMPLE: 1) .00135 2)  .00135 3) 001.35 4) 1.35 x 10-³ *There's a negative to show that it WAS a small number before. 

  8. Questions for scientific notation If the exponent on the 10 is negative, is the original number big or small? It means that the original number was small

  9. Units Units are parts of a measurement that tells us what scale or standard is being used to represent the results to the measurement The two most widely used systems are the English system and the metric system if no one has their own sets of units, complete chaos would result

  10. English system • used in the United States • ex: pounds, ounces, cups, feet, inches, miles

  11. Metric/SI system  -most of the world uses this  -ex: meters,grams,kilometers,centimeters, liters  -SI system also called International system  -SI system is based on metric system                                                                                       __                                                                              |                                                                             |                                                                            cm                                                                             |                                                                              |__

  12. Example questions 1)Explain the differences between the metric system and the English system? The metric system is used all over the world except for America. 2)What is the meaning(10^?) for deci? The meaning of deci is 10^-1 or 0.1m.

  13. The unit used for measuring length in the SI system is meters. **Every ruler has two systems on it. One side with centimeters and the other with inches. 1 inch = 2.54 cm Measurements of length

  14. Prefixes for measurements • The size of the measurements are purely in their prefix. If there’s a kilo that means there’s 1000 m. If it’s centimeters then there’s 0.1 m. USE THIS: King Henry Died drinking Chocolate Milk Kilo hecto deca deci centi milli

  15. The unit used for measuring volume in the SI system is liters. 1 millilter = 0.001 liters The unit used for measuring mass (weight) in the SI system is grams. Scientists use a balance to determine the mass of an object. Measurements of mass and volume

  16. << Mass Volume >>

  17. Questions for measurements • What is 10m written in kilometers? .001 km

  18. 1.    Problem-Solving Strategy Be systematic Ask questions - Where do we want to go? - What do we know? - How do we get there? - Does it make sense?

  19. Example Question: Why should you ask yourself problem-solving strategy questions? Answers: You should ask yourself problem-solving strategy questions because you should make sure your answers are correct and logical. 

  20. Converting Units

  21.        2.    Converting Units of Measurement                   Use conversion factor to change one unit to another -  Conversion factor is a ratio to convert from one unit to another               - Conversion factor are built from an equivalence statement               - Shows relationship between units in different system               - Possible conversion factor: 2.54cm/1in or 1in/2.54cm                   Choosing Conversion Factor -  Choose a conversion factor that cancels the units we want to eliminate - Leave units we want in results -         Choose which to use by looking at the direction of the require change

  22. Pesos  Dollars

  23. 3.    Tools for Converting from One Unit to Another                 State some general steps for doing conversions by dimensional analysis -  Step 1. Convert one unit to another, use equivalence statement. The conversion factor needed is a ratio of the two part of the equivalence statement - Step 2. Choose appropriate conversion factor by looking at the required change - Step 3. Multiply quantity to be convert by the conversion factor to give quantity with desire units - Step 3. Make sure you have correct numbers of significant figures

  24. QUIZ SLIDE! • How do you write 4,512 in scientific notation? • Describe why the unit is necessary for a measurement. • What is the meaning (10^?) for micro?  • What are the tools in our problem-solving strategy used for? • Which metric unit should be used to measure the distance between Albertsons and La Quinta?

  25. Answers for quiz ! • 4.512 x 10³ • If you don't have the unit for the measurement, then chaos would result.   • The meaning of micro 10^-6 or 0.0000001. • The tools in our problem-solving strategy is used for converting one unit to another • The unit should be kilometers

  26. URL links • http://www.deltamxscam.com/PESOS.jpg • http://www.businesspundit.com/wp • content/uploads/2009/02/dollars.jpg • http://www.snap-tite.com/snaptite_AED/AED_VFT/products/technical_information/conversion_tables/images/ti_conversion_tab.jpg http://3.bp.blogspot.com/_VQpW3YWt1sk/SuiqUx9NAuI/AAAAAAAAAms/EwKr7jQb1_I/s320/perfect+brow+pencil.jpg • http://www.rjdposters.com/Content/Store/404239143-Alg932.jpg • http://images.fuzing.com/members/8/83/00129883/186781.300x300.jpg - www.imageenvision.com/.../search/children/19

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