Scientific Notation

1
Scientific Notation

• Helping us write really tiny or
• really big numbers

2
Carelessness when using numbers

• I have a million math problems to do
• I have a trillion things to get done tonight
• If you win 1 million dollars and youre given the
  prize in 100 dollar bills, your stack of money
  is.
• 4 inches high

3
However

• If you win 1 trillion dollars and youre given
  the prize in 100 dollar bills, your stack of
  money is.
• 67 miles high

4
Rules to Scientific Notation

• Parts
• 1. Coefficient (mantissa) must be a number
  from 1 9.9
• 2. Exponent a power of 10
• 3.4 x 106
• Easier than writing 3,400,000

5
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

6
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

7
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

8
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

9
Be Careful

• Remember the rule about the coefficient!
• Ex. (4.0 x 103) x (3.0 x 104) 12.0 x 107
• WRONG!!!
• Answer 1.2 x 108

10
Math Operations Sci. Notation

• For Addition and Subtraction
• must make the exponents the same
• Ex. 5.4 x 103 6.0 x 104
• 0.54 x 104
• 6.0 x 104
• 6.5 x 104

11
Special Note

• Sometimes exponents are written differently.
• We are used to 3.4 x 105
• However, you may see 3.4E5
• It means the same thing (E represents the
  exponent and replaces x 10