Scientific Notation

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Scientific Notation
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Scientific Notation

• A number is in scientific notation when
• There is a number (Ill call n) that is bigger
  than or equal to one, but less than ten.
• This number n is multiplied by a power of ten.
• A power of ten is 10 to the something power.
• So it will look something like this
• N x 10

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Examples

• Yes
• No
• No
• No
• Yes

• Which are in scientific notation?
• 3.5 x 103
• 62.6 x 10-2
• 0.86 x 108
• 3.82 x 100-6
• 4.6 x 100

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Writing Numbers in Scientific Notation

• Move the decimal so that the new number is
  greater than or equal to one, but less than ten
  (so that there is one nonzero number to the left
  of the decimal).
• Count the number of places you moved the decimal
  (This will be the exponent of 10)
• If the number started out bigger than one, the
  exponent will be positive.
• If the number started out less than one, the
  exponent will be negative.

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Examples

• Write in scientific notation
• 13,030,000
• 0.000 092
• 0.003 5
• 4,825,000,000
• 675 million
• 283 hundred thousandths

• 1.303 x 107
• 9.2 x 10-5
• 3.5 x 10-3
• 4.825 x 109
• 6.75 x 108
• 2.83 x 10-3

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To change to a standard number

• Look at the exponent on the 10.
• If it is positive, MOVE the decimal that many
  places to the right.
• If it is negative, MOVE the decimal that many
  places to the left.

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Examples

• Write as a standard number
• 3.84 x 106
• 6.2 x 10-5
• 5 x 10-3
• 1.2345 x 1010
• 7.91 x 100
• 5 x (7 x 106)

• 3,840,000
• 0.000 062
• 0.005
• 12,345,000,000
• 7.91
• 35,000,000

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Powers of 10

• When the exponent is positive, it is telling you
  how many zeroes you will have.
• When the exponent is negative, it is telling you
  how many places you will have in the number.

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Examples

• 106
• 10-3
• 107
• 10-5
• 0.00001
• 10,000
• 100,000,000,000
• 0.01

• 1,000,000
• 0.001
• 10,000,000
• 0.00001
• 10-5
• 104
• 1011
• 10-2

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