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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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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:
    • A number between 1 and 10 (only 1 digit to the left of the decimal!)
    • Ten raised to a power
slide3

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

slide4

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

adding and subtracting using scientific notation
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

multiplying and dividing using scientific notation
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
units of measure
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
slide9
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
slide10
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
derived units
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.
slide12
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