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Understanding the Metric System: Unit Conversions and Scientific Notation in Physics

This lesson focuses on practice with the metric system, emphasizing conversions between units such as grams to kilograms and liters to milliliters. Students will engage in dimensional analysis, exploring how units interact during addition, subtraction, multiplication, and division. The session will cover scientific notation, demonstrating its utility for handling very large and small numbers in physics. Engaging activities will facilitate understanding of measurement and the metric system's advantages, enhancing students' mathematical skills in scientific contexts.

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Understanding the Metric System: Unit Conversions and Scientific Notation in Physics

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  1. Bellwork • On the left side of your notebook, write the measurements using the desired metric prefix: • 2,400 gm = ______ kg • 4 L = ______ mL • 660 nm = __________ m • 9.8 s = __________ ps

  2. Physics 9/13/13 • What’s up today? • Metric System Practice (if needed) • Dimensional Analysis • How Many Light-years is your Pencil?

  3. Metric System • 5.42x106 m = ________ Mm • 4.20x10-5 m = ________ μm • 2.1x10-10 m = ________ nm = _________ fm

  4. Dimensional Analysis • Physicists don’t just add numbers…as wonderful and fascinating as they are. • How do we do math with units?

  5. Arithmetic • Rule 1: We can only add or subtract same units. Not okay: 20 kg + 300 m = ???

  6. Arithmetic • Rule 2: Multiplying or dividing with units results in…wait for it…

  7. Arithmetic • Rule 2: Multiplying or dividing with units results in…wait for it…multiplying or dividing with units. ]

  8. Arithmetic • Rule 3: Squaring or taking a root of a unit results in….

  9. Arithmetic • Rule 3: Squaring or taking a root of a unit results in….squaring or taking a root of a unit.

  10. Arithmetic • Rule 4: We cannot have a unit in the argument of an exponential, log, or trig function.

  11. Unit Conversion • How to convert from one unit to another?

  12. Unit Conversion • How to convert from one unit to another? • Chaining! • Go from m to cm to mm:

  13. Unit Conversion • Chemistry:

  14. Your turn. • Rest of class: activity time. • Read instructions, perform measurements in small groups. • If an instrument is being used, skip and come back. • Ask Mr. Abbott for help!!!!!

  15. Scientific Notation • In physics, we use some very BIGand some very small numbers. • Charge of an electron: .000000000000000001602 C • Distance to the Sun: 149,700,000,000 m

  16. Scientific Notation • There has to be a better way!

  17. Scientific Notation • There has to be a better way! • Scientific notation. • Taking advantage of the “powers” of powers of ten…

  18. Scientific Notation • Easy example: • Write 2,000 in scientific notation. • Easy-ish: • Write 20,200 in scientific notation. • Not-quite-as-easy: • 299,800,000 • Tough-ish: • 0.00000913

  19. Scientific Notation • Want more detail? • Base-ten number system: ANY number in the system can be represented by adding multiples of powers of ten: 22,531 • Base-two number system: binary code. 001101

  20. Scientific Notation • Convenience of base-ten? • Can ALSO represent any number as a number b/w 1 and 10 multiplied by some power of ten:

  21. Metric System • The metric system takes advantage of powers of ten to make it easier to express units. • Every power of ten (103, 106, 10-3) has it’s own prefix (kilo, mega, milli).

  22. Metric System • The metric system takes advantage of powers of ten to make it easier to express units. • Every power of ten (103, 106, 10-3) has it’s own prefix (kilo, mega, milli). • Activity time!

  23. Next time… • Dimensional analysis. • How many lightyears long is a pencil?

  24. Roadmap: • After dimensional analysis, we move into basic math (functions and graphing). • THEN we start talking MOTION! Huzzah!

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