Download Write numbers in Decimal Form (standard notation)

Learning Target: I can read and write numbers and perform operations in Scientific
Notation.
Powers of Ten video: http://www.wimp.com/scaleuniverse/
Multiplying by a power of ten is easily done by moving the decimal point!
Scientific notation is a shorter way to write very large or very small numbers.
Scientific notation is written as a number between 1 and 10 10
positive exponents are used for numbers greater than 1
negative exponents are used for numbers less than 1
****Write numbers in Decimal Form (standard notation)****
(1) Move the decimal point to the right for positive exponents of 10.
3.03 104  30,300.
(2) Move the decimal point to the left for negative exponents of 10.
3.03 104  0.000303
(3) *** 10 0  1 ; try it with calculator: 10 0  1 ***
Change into decimal form (standard notation):
3.4506  105 = 345,060
5.024 103 = 5,024
3.4506 105 = 0.000034506
5.024 103 = 0.005024
****Write numbers in Scientific Notation****
(1) Place a decimal point to the right of the first nonzero number.
(2) Count the number of decimal places the decimal has “moved” from its
original location. This will be the exponent of the 10.
(3) If the original number was less than 1, the exponent is negative.
If the original number was greater than 1, the exponent is positive.
Change into scientific notation:
423 =
4.23  102
0.423 =
4.23 101
98,000,000 =
0.0098 =
9.8  107
9.8 103
Interactive practice: http://janus.astro.umd.edu/astro/scinote/
Operations with Scientific Notation
Parts of an expression written in Scientific notation:
1.23  10 6
To multiply terms in Scientific Notation
1) multiply the coefficients
2) then use the multiplication property of exponents to multiply the powers of ten
(To multiply powers with the same bases ADD the exponents.)
https://learnzillion.com/lessons/1293-multiply-numbers-in-scientific-notation
Sometimes you will end up with numbers that are no
longer in Scientific Notation – you NEED to change
your answer into Scientific Notation:
 2.3 10 1.8 10 
3
6
1.4 10  7.6 10 
4
(1.4  7.6)  (104 103 )
(2.3  1.8)  (103 106 )
10.64 107
4.14 10
1.064 107 1
9
3
1.064 108
To divide terms in Scientific Notation
1) divide the coefficients
2) then use the division property of exponents to divide the powers of ten
(To divide powers with the same bases SUBTRACT the exponents)
https://learnzillion.com/lessons/1313-divide-numbers-in-scientific-notation
 5.2 10 
1.3 10 
3
1
REAL LIFE EXAMPLE:
In 1867 the US purchased Alaska from Russia for
$7.2 million. The total are of Alaska is about
5.9  105 square miles. What was the price per
square mile?
7.2million  7, 200, 000  7.2 106
(5.2  1.3)  (1031 )
 7.2 10 
 5.9 10 
4  102
(7.2  5.9)  (1065 )
6
5
1.22 102
$12.20 per square mile