Objective The student will be able to:

1
ObjectiveThe student will be able to
express numbers in scientific and decimal
notation.
2
How wide is our universe?

• 210,000,000,000,000,000,000,000 miles
• (22 zeros)
• This number is written in decimal notation. When
  numbers get this large, it is easier to write
  them in scientific notation.

3
Scientific Notation

• A number is expressed in scientific notation when
  it is in the form
• a x 10n
• where a is between 1 and 10
• and n is an integer

4
Write the width of the universe in scientific
notation.

• 210,000,000,000,000,000,000,000 miles
• Where is the decimal point now?
• After the last zero.
• Where would you put the decimal to make this
  number be between 1 and 10?
• Between the 2 and the 1

5
2.10,000,000,000,000,000,000,000.

• How many decimal places did you move the decimal?
• 23
• When the original number is more than 1, the
  exponent is positive.
• The answer in scientific notation is
• 2.1 x 1023

6
1) Express 0.0000000902 in scientific notation.

• Where would the decimal go to make the number be
  between 1 and 10?
• 9.02
• The decimal was moved how many places?
• 8
• When the original number is less than 1, the
  exponent is negative.
• 9.02 x 10-8

7
Write 28750.9 in scientific notation.

• 2.87509 x 10-5
• 2.87509 x 10-4
• 2.87509 x 104
• 2.87509 x 105

8
2) Express 1.8 x 10-4 in decimal notation.

• 0.00018
• 3) Express 4.58 x 106 in decimal notation.
• 4,580,000
• On the graphing calculator, scientific notation
  is done with the button.
• 4.58 x 106 is typed 4.58 6

9
Write in PROPER scientific notation.(Notice the
number is not between 1 and 10) 8) 234.6 x 109

• 2.346 x 1011
• 9) 0.0642 x 104
• on calculator 642
• 6.42 x 10 2

10
Write 531.42 x 105 in scientific notation.

1. .53142 x 102
2. 5.3142 x 103
3. 53.142 x 104
4. 531.42 x 105
5. 53.142 x 106
6. 5.3142 x 107
7. .53142 x 108

11
Scientific Notation

• Quick Review

12
Powers of 10

• http//micro.magnet.fsu.edu/primer/java/scienceopt
  icsu/powersof10/
• http//www.powersof10.com/
• Powers of 10 - Google Videos

13
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
14
Question 6
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
15
Question 14
Write 4.953 x 104 in standard form
Write the decimal number.
4.953
Move the decimal the number of places specified
by the powers of ten to the right since it is
positive.
4 9530
X 104
4 Places
Rewrite the number in integer/standard form.
49,530
16
Question 17
Write 8.397 x 10-1 in standard form
Write the decimal number.
8.397
Move the decimal the number of places specified
by the powers of ten to the left since it is
negative.
0 8 397
X 10-1
1 Place
Rewrite the number in integer/standard form.
0.8397
17
Multiplying and Dividing With Your Calculator

• Punch the number (the digit number) into your
  calculator.
• Push the EE or EXP button. Do NOT use the x
  (times) button!!
• Enter the exponent number. Use the /- button to
  change its sign.
• Voila! Treat this number normally in all
  subsequent calculations.
• Scientific Calculator
• Scientific calculator for chemists with notebook
• http//www.calculator.com/calcs/calc_sci.html

18
Scientific Notation Tutorials

• http//www.wwnorton.com/college/chemistry/gilbert/
  tutorials/ch1.htm
• (Click on Scientific Notation Link - view
  tutorial)
• http//www.visionlearning.com/library/module_viewe
  r.php?mid47lc3
• (Read Scientific Notation towards the bottom of
  the page)
• http//www.wtamu.edu/academic/anns/mps/math/mathla
  b/col_algebra/col_alg_tut3_scinot.htm