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2.1 - Scientific Notation

2.1 - Scientific Notation. Scientific Notation. Numbers that are extremely large can be difficult to deal with… sooo Scientists convert these numbers into scientific notation Scientific notation expresses numbers as a multiple of two factors:

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2.1 - Scientific Notation

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  1. 2.1 - Scientific Notation

  2. Scientific Notation • Numbers that are extremely large can be difficult to deal with…sooo • Scientists convert these numbers into scientific notation • Scientific notation expresses numbers as a multiple of two factors: • A number between 1 and 10 (only 1 digit to the left of the decimal!) • Ten raised to a power

  3. For example: A proton’s mass =0.0000000000000000000000000017262 kg If you put it in scientific notation, the mass of a proton is expressed as 1.7262 x 10-27 kg Remember: When numbers larger than 1 are expressed in scientific notation, the power of ten is positive When numbers smaller than 1 are expressed in scientific notation, the power of ten is negative

  4. Try these: Convert 1,392,000 to scientific notation. = 1.392 x 106 Convert 0.000,000,028 to scientific notation. = 2.8 x 10-8

  5. Adding and Subtracting using Scientific Notation • Make sure the exponents are the same!! 7.35 x 102 + 2.43 x 102 = 9.78 x 102 • If the exponents are not the same, you have to make them the same!! • Tip: if you increase the exponent, you decrease the decimal ----- if you decrease the exponent, you increase the decimal • Example: Tokyo pop: 2.70 x 107 Mexico City pop: 15.6 x 106 = 1.56 x 107 Sao Paolo pop: 0.165 x 108 = 1.65 x 107 NOW you can add them together and carry thru the exponent Total= 5.91 x 107

  6. Multiplying and Dividing using Scientific Notation • Multiplication: • Multiply decimals and ADD exponents • Ex : (1.2 x 106) x (3.0 x 104) = 3.6 x 1010 6 + 4 = 10 • * Ex: (1.2 x 106) x (3.0 x 10-4) = 3.6 x 102 6 + (-4) = 2 • Division: • Divide decimals and SUBTRACT exponents • Ex: (5.0 x 108) ÷ (2.5 x 104) = 2.0 x 104 8 – 4 = 4 • *Ex: (5.0 x 108) ÷ (2.5 x 10-4) = 2.0 x 1012 8 – (-4) = 12

  7. 2.2-2.3 - Measurements and Units

  8. Units of Measure • SI units: SystemeInternationale d’ Unites • standard units of measurement to be understood by all scientists • Base Units: defined unit of measurement that is based on an object or event in the physical world • there are 7 base units • some familiar quantities are time, length, mass, and temp

  9. Time • second (s) • Many chemical reactions take place in less than a second so scientist often add prefixes, based on multiples of ten, to the base units. • ex. Millisecond Length • meter (m) • A meter is the distance that light travels though a vacuum in 1/299 792 458 of a second. • What is a vacuum? • Close in length to a yard. • Prefixes also apply…ex. millimeter

  10. Mass • mass is a measurement of matter • kilogram (kg) • about 2.2 pounds • Masses measured in most laboratories are much smaller than a kilogram, so scientists use grams (g) or milligrams (mg). • How many grams are in a kilogram? • 1000 • How many milligrams are in a gram? • 1000

  11. Derived Units • Not all quantities are measured in base units • A unit that is defined by a combination of base units is called a derived unit. • Volume and Density are measured in derived units.

  12. Volume • The space occupied by an object • Unit = cm3 = mL • Liters are used to measure the amount of liquid in a container (about the same volume as a quart) • Prefixes also applied…ex. milliliter

  13. Modified Table 2.1 – The Base Units

  14. Modified Table 2.2 – SI Prefixes

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