Download Physical Science 20 Notes Unit 1 Part 1B

1. Scientific Notation
is used due to the large and small numbers used by scientists. For example
the nearest star to our solar system is 41 500 000 000 000 000 000 mm.
We do not write this number this way but use scientific notation to shorten
the way the number is written which is 4.15 x 1019mm
In this notation a number has the form
M x 10n
Where the M is a number and n is called index or exponent and is a positive
or negative number.
To change a number into scientific notation
a) Determine the number M by moving the decimal point so that you
leave only one non zero digit to the left of it.
b) M contains all the significant digits indicated by the measurement.
(We will discuss this later)
c) Determine the index n by counting the number of places you have
moved the decimal point. If the decimal is moved to the left n is
positive and if moved to the right n is negative.
Example #1 Convert to Scientific Notation
a) 48000 = 4.8 x 104
b) 7330000 = 7.33 x 106
c) 0.000345 = 3.45 x 10-4
d -0.00000056 = -5.6 x 10-7
e) 3567000 =
f) 0.00005677 =
g) -678 =
h) -0.000000000000345 =
Example #2 Convert into an ordinary number
a) 5.56 x 104 = 55600
b) 4.78 x 10-6 = 0.00000478
c) -4.67 x 10-4 = -0.000467
d) -3.678 x 109 = -3678000000
e) 4.67 x 10-12 =
f) -6.78 x 1015 =
g) -8.9 x 107 =
h) -561 x 10-15 =
Assignment
Question #’s 1 and 2 from handout
Scientific Notation Operations
a) Multiplication and Division using Scientific Notation
Recall Laws of Exponents
1. Multiplication Law
(xa)(xb) = xa+b
2. Divison Law
(xa)÷(xb) = xa-b
3. Power
(xa)b = xab
Examples on board
When multiplying numbers expressed in scientific notation, the exponents of
powers of 10 are added even if they are not the same. You multiply the
numbers preceding the powers of 10 and then add the exponents to get the
product.
For example
(4.3 x 104)(6.2 x 105) = 26.7 x 109. This value must then be
completely simplified to 2.67 x 1010.
Additional examples on board.
When dividing you follow similar steps as in multiplication except the
exponents are subtracted.
For example
(4.3 x 104)(6.2 x 105) = 0.69 x 10-1 = 6.9 x 10-2
Additional examples on board.
Assignment
Question # 3 from handout
b) Addition and Subtraction
When adding or subtracting numbers expressed in scientific notation the
values of the exponents must first be converted to similar values and then
the numbers preceding the powers of 10 can be added or subtracted.
For example
1. 4.3 x 104 + 6.2 x 105 = 0.43 x 105 + 6.2 x 105 = 6.63 x 105
2. 4.3 x 104 – 6.2 x 105 = 0.43 x 105 – 6.2 x 105 = -5.77 x 105
Additional examples on board
Assignment
Question #’s 4 and 5 from handout