Scientific Notation and Powers of Ten

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Scientific Notationand Powers of Ten

• 7th grade math

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Powers!!

• Power is a way to write a multiplication problem.
• It has two parts base and an exponent
• Base (big )
• Exponent (tiny )

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Base and Exponent

• BE
• Base is the you multiply.
• Exponent is how many times you multiply it.

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Example

• 53 5 x 5 x 5 125
• 64 6 x 6 x 6 x 6 1296

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Examples w/ exponent of 1

• Anytime 1 is your exponent, the base remains the
  same
• 61 6
• 2151 215

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Examples w/ exponent of 0

• Anytime zero is your exponent, your answer is 1.
• 50 1
• 7580 1

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Power of Ten

• Vocabulary
• Standard form traditional (normal) way to write
  numbers
• Scientific Notation shorthand sciency way to
  write numbers

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Power of Ten

• When you have a problem that uses a power of ten,
  then you will move the decimal right that many
  places
• Example
• 48 x 105 4,800,000 (you moved the decimal 5
  places right)
• 7.29 x 104 72,900 (you moved the decimal 4
  places right)

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Power of Ten

• Writing numbers in scientific notation.
• 428,000 4.28 x 105
• Why? ---- You move the decimal so that 1 non
  zero number is in the ones spot and count how
  many places you had to move it--- that number
  becomes your exponent.

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Negative Powers

• When you have a problem that uses a negative
  power of ten, then you will move the decimal left
  that many places
• Example
• 4.8 x 105 .000048 (you moved the decimal 5
  places left)
• 7.29 x 10-4 .000729 (you moved the decimal 4
  places left)

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Negative Powers

• Writing numbers in scientific notation.
• .0028 2.8 x 10-3
• Why? ---- You move the decimal so that 1 non
  zero number is in the ones spot and count how
  many places you had to move it--- that number
  becomes your exponent.