Scientific Notation and Matter

Scientific Notation
Usually used to write extremely small or large numbers. The number is always between one and ten, and multiplied to a power of 10  Written in the form the form X * 10²

Ex: 145 = 1.45 * 10²

                  OR

      0.0145 = 1.45 * 10^-2 
***When moving to the Left    Positive Exponent
      When moving to the Right    Negative Exponent
ROUNDING: Always be sure to round ONLY at the end of the equation.
Practice:
a)Write 36400 in scientific notation
b)Write  1.5 x 10⁵  in decimal notation
c)Write 0.0000000000523 in scientific notation
d)Write 2.3 x 10^-3 in decimal (normal) notation
Answers:
a) 3.64 * 10⁴

b) 150000

c) 5.23 * 10^-11

d) 0.0023

Adding and Subtracting

When adding or subtracting Scientific Notation, change the number to decimal notation, and then add, and then return number to Scientific Notation.

Ex: (2 * 10^3) + (16 * 10^3) = 2000 + 16000 = 18000 = 1.8 * 10^3

Practice:

a) (6 * 10^5) + (3 * 10^5)

b)7.3 * 10^2) - (6 * 10^2)

Answers:

a)600000 + 300000 = 900000 = 9 * 10^5

b) 7300 - 6000 = 1300 = 1.9 * 10^2

Multiplying and Dividing
When multiplying or dividing, add or divide the two numbers, and if multiplying, add the powers of ten. If dividing, subtract the powers of 10.
Ex: (2 * 10^3) (4 * 10^7) = 2*4 = 8,  3+7 = 10 = 8 * 10^10
Practice:
a) (3 * 10^6) (3 * 10^5)
b) (8 * 10^6) / (2 * 10^4)
Answers
a) 3 * 3 = 9, 6+5 = 11   9 * 10^11
b)8/2 = 4. 6-4 = 2  4*10^2

Scientific Notation Review.

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