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
![Right arrow Right arrow](http://officeimg.vo.msecnd.net/en-us/files/120/764/ZA006052154.gif)
Ex: 145 = 1.45 * 102
OR
0.0145 = 1.45 * 10-2***When moving to the Left
![Right arrow Right arrow](http://officeimg.vo.msecnd.net/en-us/files/120/764/ZA006052154.gif)
When moving to the Right
![Right arrow Right arrow](http://officeimg.vo.msecnd.net/en-us/files/120/764/ZA006052154.gif)
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
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
![Right arrow Right arrow](http://officeimg.vo.msecnd.net/en-us/files/120/764/ZA006052154.gif)
b)8/2 = 4. 6-4 = 2
![Right arrow Right arrow](http://officeimg.vo.msecnd.net/en-us/files/120/764/ZA006052154.gif)
Scientific Notation Review.