Scientific Notation

1
Scientific Notation

• Making large and small numbers more manageable.

2

• Scientific notation is a system for representing
  a number as a number between 1 and 10 multiplied
  by a power 10.
• Scientific nation is most useful for presenting
  very large or very small numbers in a form that
  is easier to use.
• For example The sets of numbers below are
  equivalent. However, the numbers of the right
  can be read much more easily.
• 253,000,000,000,000,000,000 2.53 x 1020
• 0.0000000000000000000253 2.53 x 10-20

3

• In scientific notation, numbers are expressed as
  a number between 1 and 10 multiplied by 10 raised
  to an exponent.
• 120.3 1.203 x 100
• 100 is the same as 102

4

• In scientific notation, numbers are expressed as
  a number between 1 and 10 multiplied by 10 raised
  to an exponent.
• 120.3 1.203 x 102
• 100 is the same as 102

5

• In scientific notation, numbers are expressed as
  a number between 1 and 10 multiplied by 10 raised
  to an exponent.
• 1203 1.203 x 1000
• 1000 is the same as 103

6

• In scientific notation, numbers are expressed as
  a number between 1 and 10 multiplied by 10 raised
  to an exponent.
• 1203 1.203 x 103
• 1000 is the same as 103

7

• In scientific notation, numbers are expressed as
  a number between 1 and 10 multiplied by 10 raised
  to an exponent.
• 0.1203 1.203 x 10-1
• 1/10 is the same as 10-1

8

• In scientific notation, numbers are expressed as
  a number between 1 and 10 multiplied by 10 raised
  to an exponent.
• An easy way to determine the exponent of ten is
  to count the decimal positions you move.
• 0.000001203 1.203 x 10-6
• The decimal has moved backwards 6 positions

9

• In scientific notation, numbers are expressed as
  a number between 1 and 10 multiplied by 10 raised
  to an exponent.
• An easy way to determine the exponent of ten is
  to count the decimal positions you move.
• 1203000000 1.203 x 109
• The decimal has moved forwards 9 positions

10

• Practice Questions
• 74,390,000 __________ x 10_
• 0.000009998 _________ x 10_
• -0.0000623 __________ x 10_
• 5.466 x 106 __________
• 2.3 x 10-4 ___________

11

• Scientific notation makes it easier to express
  very large or very small numbers in more
  manageable terms. It is used widely in the
  scientific community when referencing everything
  from numbers of bacterial to concentrations of
  solution.

12
Concept Question

• How would you express a number such as 1.5 or 0.2
  in scientific notation?