Scientific Notation

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Scientific Notation

• Writing large and small numbers

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Its easy to make mistakes when computing with
small numbers such as 0.000022 and large numbers
such as 75,000,000. People who deal regularly
with such numbers use scientific notation.

• Scientific notation a method of writing very
  large and very small numbers using powers of 10.
• Take for example, an ordinary penny contains
  about 20,000,000,000,000,000,000,000 atoms. The
  average size of an atom is about 0.00000003
  centimeters across

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Written in scientific notation

• Number of atoms in a penny
• 2.0 x 1022
• Size of each atom
• 3.0 x 10-8
• The sign on the exponent tells which direction to
  move the decimal. A positive exponent means move
  the decimal to the right, and a negative exponent
  means move the decimal to the left.

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Writing Scientific Notation

• Scientific notation is written using the product
  of 2 factors.
• 1.0 x 106 1,000,000
• First factor is a number 1 but lt 10.
• 1,000,000 1.0
• Second factor is a power of 10 (106)

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Scientific Notation to Standard Notation

• Write each number in standard notation.
• 2.64 x 107
• 2.64 x 10,000,000 107 10,000,000
• 26,400,000 Think Move the decimal right 7
  places for positive exponent.
• 1.35 x 10-4
• 1.35 x 1/10,000 10-4 1/10,000
• 0.000135 Think Move the decimal left 4
  places for negative exponent.

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Standard Notation toScientific Notation

• Write each number in scientific notation.
• 0.000002
• 2 Move the decimal to get a number between 1
  and 10
• 2 x 10? Set up scientific notation. Think
  decimal needs to move left 6 places to change
  2 to 0.000002, moving left makes exponent
  negative.
• 2 x 10-6
• 0.0027
• 2.7 Move the decimal to get a number between 1
  and 10
• 2.7 x 10? Set up scientific notation. Think
  decimal needs to move left 3 places to
• change 2.7 to 0.0027, moving left makes
  exponent negative.
• 2.7 x 10-3

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Scientific Notation with a Calculator

• Technology Lab with TI-83
• calculator

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Scientist often have to work with very large or
very small numbers. For example, the Andromeda
Galaxy contains over 200,000,000,000 (billion)
stars. Scientific notation is a compact way of
expressing these numbers.

• Show 200,000,000,000 in scientific notation on
  your graphing calculator.
• Enter 200,000,000,000 on your calculator. Press
• ENTER

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2E11 on the graphing calculator display means 2
x 1011

• Your calculator automatically puts very large
  numbers into scientific notation.

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You can enter scientific notation directly into
the calculator yourself using the EE function
key(2nd key then comma , key).

• Enter 2 x 1011 by pressing 2 2nd EE , 11
  enter

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Evaluating Expressions using Scientific Notation

• Evaluate 230,000,000 x 650,000
• First write 230,000,000 in scientific notation
  2.3 x 108
• Second write 650,000 in scientific notation 6.5
  x 105
• Press 2.3 2nd EE , 8 x 6.5 2nd EE , 5
  enter
• In scientific notation, 230,000,000 x 650,000 is
  equal to 1.495 x 1014 or 149,500,000,000,000
• (149 trillion, 500 billion).

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Evaluate (340,000,000,000 1,235) x 4,568

• Write each number in scientific notation.
• 340,000,000,000 3.4 x 1011
• 1,235 1.235 x 103
• 4,568 4.568 x 103
• Press (3.4 2nd EE , 11 1.235 2nd EE , 3
  ) x 4.568 2nd EE , 3 enter
• (340,000,000,000 1,235) x 4,568
• 1.257587045 x 1012
• (because this calculator displays results to only
  10 decimal places, this in not exact. The exact
  answer is 1.2575870445344110 x 1012)

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Problem Solving

• In space, light travels about 9,460,000,000,000
  kilometers per year. This distance is known as a
  light-year. The star Altair is 16.3 light-years
  from earth. Write this distance in scientific
  notation.
• Suppose the universe is made up of
  125,000,000,000 galaxies, each containing
  200,000,000,000 stars. Use this data to find the
  total number of stars in the entire universe.
  Express your answer in scientific notation and in
  standard form.

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Answer (check out what these would look like in
standard notation)

• 1.54E14 kilometers from earth
• 2.5E22 star in the universe

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154,000,000,000,000154 trillion kilometers

• 25,000,000,000,000,000,000,000
• 25 sextillion stars in the universe

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Extremely small numbers are written in the same
way but use (-) negative exponents.

• For example, our ordinary penny contains about 20
  sextillion atoms, written
• 2.0E22 or 20,000,000,000,000,000,000 atoms
• The average size of the atom we discussed earlier
  is about 3 hundred millionths centimeters across,
  written
• 3.0E-8 or 0.00000003 centimeters

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Helpful Hint

• The sign of the exponent tells which direction to
  move the decimal.
• A positive exponent means to move the decimal to
  the right.
• A negative exponent means move the decimal to the
  left.

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Math Fact !!!!!

• The mass (weight) of the earth is about
  5,980,000,000,000,000,000,000,000 kilograms.
• (5 septillion, 980 sextillion)
• This is written in scientific notation as
• 5.98 x 1024
• How would you enter this into your calculator?

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Ever wonder what 1 million pennies looks
like?Heres your answer.