Transcript Scientific Notations

SCIENTIFIC NOTATION
• In scientific notation, a number is
written as the products of two
numbers:
• a coefficient and some power of
10
SCIENTIFIC NOTATION CONTINUED
• The general form for scientific
notation is:
• M x 10n where
• M is  1 but < 10
• n is an integer and exponent
• {integers must be a positive or
negative whole number}
RULES FOR SCIENTIFIC NOTATION
. Determine “M” by moving the decimal
point in the original number to the left or to
the right so that only one non-zero digit
remains to the left of the decimal
• 1
GUIDED PRACTICE
• Express the following in scientific
notation:
• 1, 400, 000 km, the distance to the
sun
• 0.000 000 000 066 7, the Universal
Gravitational Constant
RULES FOR SCIENTIFIC NOTATION
. Determine “n” by counting the number of
places that the decimal point was moved. If
the decimal was moved to the left, n is
positive; if the decimal is moved to the right, n
is negative
• 2
INDEPENDENT PRACTICE
• Express the following in scientific notation:
• a. 85 000 000
• b. 0.000 9
• c. 74 000
• d. 0.000 005
• e. 30 000 000
• f. 864 000
RULES FOR CALCULATIONS INVOLVING SCIENTIFIC
NOTATION
Addition/Subtraction: In order to add or
subtract numbers in scientific notation, the
numbers must be expressed in the same
exponent or “n”
• 1.
RULES FOR CALCULATIONS INVOLVING SCIENTIFIC
NOTATION
• Example: 6.3 x104 + 2.1 x 105
• 1) Convert one number to the
same exponent
• 2) Add the number
SOLUTION
• 6.3 x104 = 0.63 x 105
• 0.63 x 105
• + 2.1 x 105
• 2.73 x105
RULE FOR MULTIPLICATION
. When multiplying, multiply the coefficients
and add the exponents together (they do
NOT have to be in the same power)
• 2
RULE FOR MULTIPLICATION
• Example: 4 x 105 * 2 x 102
•
4 x 105 * 2 x 102 = 8 x 107
RULE FOR DIVISION
• When dividing, divide the coefficients and
subtract the exponents (top exponent
minus bottom exponent)
• Example: (4 x 105) / (2 x 107)
• Ans: 2 x 10-2
COMPLETE THE FOLLOWING CALCULATIONS
• 1.
• 2.
• 3.
• 4.
(2.4 x 10-3) - (1.2 x 10-2)
(7.4 x 10-8) / (3.4 x 104)
( 3.45 x 104) * (2.3 x 103)
(3.6 x 105) + (7.82 x 104)
EXPRESS THE FOLLOWING SCIENTIFIC NOTATIONS
IN THE LONG FORM
• 1. 7 x 104
• 2. 5.3 x 104
• 3. 7 x 10-5
• 4. 4.21 x 1010
• 5. 47 000 x 105