Download Powers and Exponents

Topic: Scientific
Notation
Essential Question: What is scientific
notation and how is it used?
What is scientific notation?
• Definition: A number that is written as the
product of a factor and a power of 10. The
absolute value of the factor must be greater than
or equal to 1 and less than 10.
– Example:
What is the purpose of scientific
notation?
• It is often used to express very large or very
small numbers.
– Example:
– Example:
How is scientific notation converted to
standard form?
• The exponent tells us how many spaces to
move the decimal.
– A positive exponent implies a number greater than
1 in standard form.
• Example: 4.5 x 104 = 45,000
– A negative exponent implies a number less than 1
in standard form.
• Example: 4.5 x 10-4 = 0.00045
How is addition/subtraction completed
in scientific notation?
• Convert to standard notation, add/subtract,
and convert back to scientific notation (if
necessary).
– Example: (3 x 104) + (6 x 105)
30,000 + 600,000
630,000 = 6.3 x 105
How is multiplication completed in
scientific notation?
• Use Associative Property to group the factors
and powers of ten together.
• Multiply the factors normally.
• Use Product of Powers to simplify the powers
of ten.
– Example: (3 x 108)(3 x 104)
(3 x 3)(108 x 104)
9 x 108+4
9 x 1012
How is division completed in scientific
notation?
• Use Associative Property to group the factors
and powers of ten together.
• Divide the factors normally.
• Use Quotient of Powers to simplify the powers
of ten.
– Example: 8.6 x 1012 = 8.6 x 1012 = 4.3 x 1012-4
2 x 104
2
104
= 4.3 x 108
Summary
• Scientific notation uses a factor and power of
ten to express small & large #s. Scientific
notation can be converted to standard form.
Standard form is used to add/subtract.
Associative Property & Exponent laws are
used to multiply/divide in scientific notation.