1. Scientific Notation
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2. WARM UP
0.035 ÷ = 0.7
2) Solve 0.6 ÷ = 12
÷ = 0.11
Without changing the quotient, change
the problem so that the divisor is a whole number
÷ 0.003
It will be 68,130 ÷ 3
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3. Lets review what we learned in the earlier lesson
To divide any two decimal numbers first move the decimal point in the divisor to the right so that it becomes a whole number
Move the decimal point of the dividend the same number of places to the right as you did of the divisor
Now divide as you do with whole numbers
Put the decimal point for your answer directly above
the one in your dividend
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4. Let us take an example
9.09 ÷ 4.5
In the case of a remainder add zero to the dividend and divide until there is no remainder or until there are 4 decimal places in the answer
2.02
4.5 )
9 0
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5. Lets get started Today we are going to learn about Scientific Notation
Scientific Notation is a way to express very large or
very small numbers.
It is most often used in “scientific” calculations
where the analysis must be very precise
Scientific notation has two parts
A non zero number between 1 and 10
A power of 10
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6. What is Scientific notation ?
A number in scientific notation is written as the
product of a number between 1 and 10 (integer or
decimal ) and an integer power of 10
A number written in scientific notation has the form
N X 10r
where, N is between 1 and 10
r is an integer
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7. To Change from Standard form to Scientific notation
Place the decimal point so that there is one non zero digit to the left of the decimal point
Count the number of decimal places the decimal point
has “ moved ” from the original number. This will be
the exponent (power) of 10
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8. Standard form to Scientific notation Lets take some Examples
The power of ten indicates how many places
the decimal point has moved from the original number
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9. If the decimal point is moved N places to the left
POSITIVE EXPONENTS
100 = 1
101= 10
102 = 10 X 10 =100
10000 = 100 x 100 = x 104
If the decimal point is moved N places to the left
The power of ten is increased by N units
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10. If the decimal place is moved N places to the right
NEGATIVE EXPONENTS
1 X 10-1 = = (one tenth) 10
1 X 10-2 = = (0ne hundredth)
100
If the decimal place is moved N places to the right
then the power of 10 is decreased by N units
.01 = .01 x 100 = 1 x 10-2
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11. If the original number is less than 1, then the exponent is negative .
If the original number is greater than 1, then the exponent is
positive
579,300,000 = x 108 (Positive exponent)
= x (Negative exponents)
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12. To change Scientific notation to Standard form
Move the decimal point to the right for positive exponent 10
Move the decimal point to the left for negative exponent10
Use zeros to fill in places
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13. Lets take some examples
The decimal point has moved 6 places to the right
8.951 x 10-4 =
The decimal point has moved 4 places to the left
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14. You try some !
72,500 = x 105
27,100,000 = 2.71 x 107
5.56 x 109 = 5.56 billion
1.976 x =
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15. BREAK TIME
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16. Lets play a Game
Click on the photo to color a picture
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17. One light year is the distance light travels in one year.
If the speed of light is 3 x 105 kilometers per second,
about how many kilometers does light travel in one year ?
About 9.51 x km
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18. According to the Aluminum Association, 2,031,000,000
pounds of aluminum cans were recycled in At an
average of 29.9 cans per pound, how many aluminum cans
were recycled that year ? Express your answer in scientific
notation.
5.95 x 1010 cans
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19. Scientists divide Earth’s history in to small units based
on the types of life-forms living on then. In the Jurassic
period, which occurred about 208,000,000 years ago,
dinosaurs ruled. Express the years in scientific notation.
2.08 x 108
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20. Assessment Write each number in scientific notation:
34, x 104
165,000,000, x 1011
310, x 105
Write each number in standard form:
3.05 x
2 x ,000,000,000
9.037 x ,700,000
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21. Assessment
The distance from our sun to the nearest star, Alpha Centauri, is about 42,000,000,000,000 kilometers. Write this distance in scientific notation.
4.2 x 1013
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22. Lets review what we have learned in this lesson
Scientific notation can be expressed as the short way to write very large or very small numbers without writing all the zeros
A number in scientific notation is written as the product
of a number that is between 1 and 10 and an integer that
is power of ten
The power of ten is written with an exponent (negative or positive )
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23. To change from standard form to Scientific notation
Place the decimal point so that there is a non zero digit to the left of the decimal point
Count the number of decimal places the decimal point has “moved” from the original number
If the original number was less than 1, then the exponent is negative. If the original number is greater than 1,then the exponent is positive
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24. Lets take a few examples
(Standard form to Scientific notation)
7.8 x = 7,80,0000
( Scientific notation to standard form)
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25. You had a Great Lesson Today
Be sure to practice what you have learned today
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