Scientific Notation

1
Scientific Notation

• Scientific Notation is a specialized form of
  exponential notation.

2
Exponential Notation

• Exponential notation has a very specific format
• Coefficient X exponent
• The number 125,000 can be written different ways
  using exponential notation.

3
125,000

• 125,000 X 100
• 12,500 X 101
• 1,250 X 102
• 125 X 103
• 12.5 X 104
• 1.25 X 105
• .125 X 106
• .0125 X 107
• All of these expressions represent 125,000.

4
Scientific Notation

• Scientific Notation is similar in format. The
  only difference is in the restrictions of the
  coefficient.

5
The coefficient in Scientific Notation

• The coefficient in scientific notation is
  restricted according to the following guidelines
• 1 coefficient lt 10
• The coefficient must be equal to or greater than
  1 and less than 10.

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Numbers in scientific notation

• Correct
• (Scientific Notation)
• 2.3 X 104
• 4.65 X 10-5

• Incorrect
• (Exponential Notation)
• 23 X 103
• .465 X 10-4

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One more restriction on the coefficient

• The number of significant figures in the
  measurement determine the number of digits in the
  coefficient.

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Example

• 23,450 4 sf 2.345 X 104
• 0.00050000 5 sf 5.0000 X 10-4

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After the decimal has been moved, ask yourself

• 1. Is it a good coefficient (1Clt10 and sf)
• 2. How many times was the decimal point moved
  (this tells me what the exponent is going to be)?
• 3. Is the number greater than or less than one
  (tells me if exponent is positive (greater than)
  or negative (less than))?
• 4. Check SigFigs!

10
Handout

• Yikes

11
Working in Reverse

• It is also important to be able to write numbers
  in long form if the number is written in
  scientific notation.
• The exponent will tell you what you need to do.

12
Working in reverse

• For large numbers (have positive exponents)
• Write down the coefficient exactly as written
• Place you pen on the decimal place and move it to
  the right the number of times indicated by the
  exponent.
• Place zeros in any blank spaces
• Rewrite number neatly.

• For small numbers (have negative coefficients)
• Write down the coefficient exactly as written.
• Put your pen on the decimal place and move it to
  the left the number of times indicated in the
  exponent.
• Place zeros in any blank spaces.
• Rewrite number neatly.

13
Handout

• Yikes

14
Multiplying with numbers in sn

• When multiplying numbers in sn, follow four
  steps
• 0. Place numbers in sn
• 1. multiply coefficients
• 2. include X
• 3. add exponents to determine base 10
  exponent.
• 4. Write final answer in sn

15
Example of Multiplication

• 50,000 X 0.000020
• 0) (5 X 104) (2.0 X 10-5)
• 1) 5 X 2.0 10
• 2) X
• 3) 104 -5 10-1
• Ans 10 X 10-1 but not in sn
• 4) 1 X 101 X 10-1 1 X 100

16
Dividing with numbers in sn(very similar to
multiplication)

• When dividing numbers in sn, follow four steps
• 0. Place numbers in sn
• 1. divide coefficients
• 2. include X
• 3. subtract exponents to determine base 10
  exponent.
• 4. Write final answer in sn

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Example of Division

• 810,000,000,000,000 / 0.000,000,000,000,9
• 0) (8.1 X 1014) / (9 X 10-13)
• 8.1 / 9 0.9
• X
• 1014- -13 1014 13 1027
• ANS 0.9 X 1027 but not in sn
• 4) 9 X 10-1 X 1027 9 X 1026

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Multiplying vs. Dividing

• When multiplying numbers in sn, follow four
  steps
• 0. Place numbers in sn
• 1. multiply coefficients
• 2. include X
• 3. add exponents to determine base 10
  exponent.
• 4. Write final answer in sn

• When dividing numbers in sn, follow four steps
• 0. Place numbers in sn
• 1. divide coefficients
• 2. include X
• 3. subtract exponents to determine base 10
  exponent.
• 4. Write final answer in sn

19
Adding and Subtracting numbers in scientific
notation

• This is possible but unnecessary. We should be
  able to handle all of the adding and subtracting
  with our brains and/or our calculators.

20
Helpful Sites

• http//www.edinformatics.com/math_science/scinot6.
  htm
• http//www.edinformatics.com/math_science/scinot_m
  ult_div.htm
• http//www.edinformatics.com/math_science/scinot_m
  ult_divb.htm
• http//www.edinformatics.com/math_science/scinot_m
  ult_divc.htm
• http//janus.astro.umd.edu/astro/scinote/
• http//www.ieer.org/clssroom/scinote.html
• http//science.widener.edu/svb/tutorial/scinot.htm
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