SCIENTIFIC NOTATION

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SCIENTIFIC NOTATION

• A QUICK WAY TO WRITE
• REALLY, REALLY BIG
• OR
• REALLY, REALLY SMALL NUMBERS.

Miss Teague and Mr. Rauscher
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Mathematicians are Lazy!!!

• They decided that by using powers of 10, they can
  create short versions of long numbers.

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What is Scientific Notation?
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Rules for Scientific Notation

• To be in proper scientific notation the number
  must be written with
• a number between 1 and 10
• and multiplied by a power of
• ten
• 23 X 105 is not in proper scientific
  notation. Why?

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Step 1

• Write the decimal number.

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Step 2
Move the decimal the number of places specified
by the power of ten to the right if positive
and to the left if negative. Add zeros if
necessary.
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Step 3
Step 3 Rewrite the number in integer form.
Example (Final Answer) 3750
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Numbers Greater Than 10

• Find the number by moving the decimal point that
  is between 1 9.9
• 45,300,000 ? 4.53
• Write a positive exponent which is equal to the
  number of places you moved the decimal point to
  the left.
• 4.53 x 107

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Numbers Less Than 1

• Find the number by moving the decimal point that
  is between 1 9.9
• 0.000291 ? 2.91
• Write a negative exponent which is equal to the
  number of places you moved the decimal point to
  the right.
• 2.91 x 10-4

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• In the United States, 15,000,000 households use
  private wells for their water supply. Write this
  number in scientific notation.
• 1.5 X 107

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Your Turn
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Question 1
Write 4,776 in scientific notation
Place the decimal immediately to the right of the
left-most non-zero number. This should give you a
number between one and ten.
4.776
Count the number of digits between the old and
the new decimal point, this gives the power, n
of 10 (10n).
4 776
X 103
3 Digits
Since the decimal is shifted to the left, the
exponent is positive.
4.776 x 103
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Question 2
Write 0.0246 in scientific notation
Place the decimal immediately to the right of the
left-most non-zero number. This should give you a
number between one and ten
2.46
Count the number of digits between the old and
the new decimal point, this gives the power, n
of 10 (10n).
0 02 46
X 10-2
2 Digits
Since the decimal is shifted to the right, the
exponent is negative.
2.46 x 10-2
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Math Operations Sci. Notation

• For Division
• divide coefficients
• subtract exponents
• (6.4 x 106) / (1.7 x 102) 3.8 x 104
• 6.4 / 1.7 3.8 6 2 4

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Math Operations Sci. Notation

• For Multiplication
• multiply coefficients
• add exponents
• (3.0 x 104) x (2.0 x 102) 6.0 x 106
• 3 x 2 6 4 2 6

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Your Turn

• Using Scientific Notation,
• rewrite the following numbers.
• 0.000882
• 8.82 X 10-4
• 0.00000059
• 5.9 X 10-7
• 0.00004
• 4 X 10-5