Scientific Notation

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Scientific Notation
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Advantages of scientific notation

1. Allows for very large and very small numbers to
   be written in a more manageable form
2. It can make calculations with very large and very
   small numbers easier if a calculator is not
   available

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The general format of scientific notation is N x
10y Where 1lt N lt 10 And y indicates the number
of places and direction the decimal moves
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Positive exponents

• To convert 1234000.000 into scientific notation
  we move the decimal behind the first number.
  Count the number of places moved and that number
  becomes the exponent on the 10.

1234000 000
.
And you get
1.234000000 x 106
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To put the number back into regular notation you
move the decimal back to the right the number of
places stated by the exponents
The exponent is 4, therefore the decimal moves 4
places.
3 678
.
3 678 x 104
And you get 36780
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Negative Exponents

• To convert 0.00123 into scientific notation, we
  move the decimal behind the first non-zero digit.

The number of spaces moved becomes the exponent
on the 10, but as a negative.
0 00123
.
1.23 x 10-3
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Scientific Notation
65,000 kg ? 6.5 104 kg

• Converting into Sci. Notation
• Move decimal until theres 1 digit to its left.
  Places moved exponent.
• Large (gt1) ? positive exponentSmall (lt1) ?
  negative exponent
• Only include sig figs.

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Scientific Notation

• Calculating with Sci. Notation

(5.44 107 g) (8.1 104 mol)
Type on your calculator
5.44
7
8.1
4

671.6049383
670 g/mol
6.7 102 g/mol
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Using a Calculator

• Type in the number
• Press Exp and enter the exponent value
• DO NOT MULTIPLY BY 10. The exp does that for you.

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• Type in the number
• Press Exp and enter the exponent value
• DO NOT MULTIPLY BY 10. The exp does that for you.

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• Type in the number
• Press EE and enter the exponent value
• DO NOT MULTIPLY BY 10. The EE does that for you.

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• Type in the number
• Press 2nd x-1 and enter the exponent value
• DO NOT MULTIPLY BY 10. The 2nd x-1 does that for
  you.

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• Type in the number
• Press Exp and enter the exponent value
• DO NOT MULTIPLY BY 10. The exp does that for you.

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Copying Answers from a calculator
If answer on calculator looks like this
X
X
27
2E7
Do not write it like that!!!
Instead, write it as 2 x 107
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Practice Problems

• (7.35X10-11)(3.21X1023)(1.69X10-19)
• (9.6X103)(7.15X1015)(25.7)
• (0.000357)(757391)(250
• (7531)(2.53X1021)
• (3.576X10-5)(6.35X107)(523)
• (32571)(7.55X1057)

2.3X10-27
3.5X10-21